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# Entropy Of Air

By work I generally mean move something; useful work might be turning a drive shaft, for example, as opposed to waste heat that cannot. 026) + g*(2501 + 1. The heat death of the universe, also known as the Big Chill or Big Freeze, is a conjecture on the ultimate fate of the universe, which suggests the universe would evolve to a state of no thermodynamic free energy and would therefore be unable to sustain processes that increase entropy. Entropy cannot be destroyed (consumed), only generated and transferred from one system to another (in an isolated system, entropy can only increase). For gases, there are two possible ways to evaluate the change in entropy. Lambert, Professor Emeritus (Chemistry) of Occidental College, Los Angeles. , Steam (or Water), Nitrogen, R12, CarbonDioxide, Methane, etc. Enthalpy / ˈ ɛ n θ əl p i / (), a property of a thermodynamic system, is equal to the system's internal energy plus the product of its pressure and volume. 796 kJ/kg K = 0. 292 kJ/K (B) −0. For an isentropic process, which by definition is reversible, there is no transfer of energy as heat because the process is adiabatic, δQ = 0. It's the last day of my spring break & 13-day work sabbatical. The change in entropy is then the inverse of the temperature integrated over the change in heat transfer. This on-line psychrometric calculator makes air property determination simple. This is one example of a heat engine, which we study in this chapter. ENTROPY AND THE SECOND LAW OF THERMODYNAMICS ENTHALPY AND ENTROPY Consider this experiment: a drop of water is placed in a clean Petrie dish and the cover is put on. Bulk modulus elasticity: 1. She was trying to calm herself, sat on a barrel, and closed her eyes. Enthalpy of Formation of Various Substances. This applet calculates the thermodynamic properties of air given the pressure and entropy, pressure and density, specific energy and density, entropy and enthalpy, or pressure and temperature, in SI units (kg/m^3, J/kg, J/kg/K, m/s, Pa, K) or British Units (lb/ft^3, BTU/lbm, BTU/lbm/R, ft/s, psi, R). The Minneapolis trip became a casualty of Paige's mind boggling work schedule, The Temper Trap decided they're too good for Milwaukee, and the man in Missouri who sold me a card catalog on ebay decided he couldn't store it after all and sold it to someone else without ever telling me. In this process, air undergoes isentropic (reversible adiabatic) expansion. This is always positive, since the degree of disorder increases in the transition from a liquid in a relatively small volume to a vapor or gas occupying a much larger space. The Entropy Of Dry Air At A Given Constant Pressure? - posted in Industrial Professionals: hi, how do you calculate the entropy of air at a given pressure? this is to help me to plot my gas turbine cycle on excel Many thanks d. In general, systems tend toward greater entropy; in fact, according to the second law of thermodynamics, the entropy of an isolated system can never spontaneously decrease. That means, ∆S sys =∆S A +∆S B. DISCLAIMER: This contains Calculus. The wetter the steam, the lower the specific volume, enthalpy, and entropy will be because the dryness percentage is a factor of the 100% condition. The state function entropy S puts the foregoing discussion on a quantitative basis. UTK Award (10/01/2014 – 10/31/2014) * INVESTIGATOR TITLE SPONSOR AWARD; College of Arts and Sciences; McSween, Harry: Participation in DAWN Science Team: Regents of the Universi. Entropy Crystals will grow from the Aura in the air. The matter and its environment relevant to a particular case of energy transfer are classified as a system, and everything outside of that system is called the surroundings. Notice that water vapour, once generated, also requires more heat than dry air to raise its temperature further: 1. Going back to our solid, we saw that as we made it bigger, by adding more atoms, or hotter, by adding more packets of energy, the number of possible energy arrangements blew up. Carbon, Hydrogen, Sulfur, Nitrogen, Oxygen, Water, Methane, Carbon Dioxide, Water Vapor, Sulfur Dioxide and Air Below is a sample air calculator for TP, HP and SP input values options: Engineering Software. 948 PROPERTY TABLES AND CHARTS TABLE A-9 Properties of air at 1 atm pressure Specific Thermal Thermal Dynamic Kinematic Prandtl Temp. Entropy- Entropy is the mathematical relationship between heat and temperature, and relates to the availability of energy. Heat death does not imply any particular absolute temperature; it only requires that temperature differences. However, rational and controllable synthesize of these intrinsically complex structures remains a challenge. Calculation of thermodynamic state variables of air. where dq is a thermal energy input to the gas, du is a change in the internal energy of. I maybe have stopped posting for all this time but I never stopped listening and searching for great music. RICHARDS - ENTROPY-TEMPERATURE AND TRANSMISSION OF AIR 5 In practice expansion or compression lines lie somewhere between these two extremes and the equation of the real curve becomes povo" = pv" where n lies between 1 and 1. 0 m/s undergo a head-on collision and stick together. Many of my original plans fell through. The N99 protective mask is a basic type of mask which helps in protecting the users from around 99% of airborne particulates (PM 2. The gains of the dual-band radiation system are calculated to be 17. The term "entropy" refers to disorder or chaos in a system. the reversible and irreversible sources of entropy per unit mass of dry air. ) Calculate T 2 and the entropy generation if a real piston-and-cylinder device requires 15% more work than the internally reversible device. $\begingroup$ I found several formulas for entropy but there is no such thing as (Cpa - R), usually only Cpa Also you see, for different states the air and vapor can be in different proportions, so if the reference point is different then there will be errors, I think. 15 288 s2 =1005ln − = After compression 53 0. For example, a stack of blocks falling over will result in a lower energy state and higher system entropy. Calculation of thermodynamic state variables of air. 50 3 103 J as exhaust to a cold reservoir. in Computing and Information Systems with the University of London. For many practical reasons, from human comfort to industrial process design, the ability to determine and modify the properties of air is important. 52863609x10-2 0. Second , entropy is the measure of energy dispersal, as a function of temperature. 55 When a system undergoes a Carnot cycle, no entropy is produced within the system. Deﬁnitions 2. Note: Pay attention to the units for viscosity. in entropy of the environment. 3 μm in diameter) and saw the entropy decrease for periods lasting several tenths of a second. Entropy and poker Here are two poker hands: Specifically, the entropy of a macrostate is equal to the natural logarithm of the number of microstates in that macrostate, times a number called Boltzmann's constant. The entropy change of the air is then: ΔS air = , where Q is the heat released by the water, which is given by Equation 9. and adiabatic process is characterized by the absence of entropy, pressure change, heat exchange, or temperature change? heat exchange Your hand is warmed when you blow on it with your mouth open, but when your lips are puckered so that air expands as you blow, the air on your hand is warmer, cooler, or neither?. By work I generally mean move something; useful work might be turning a drive shaft, for example, as opposed to waste heat that cannot. The approximate entropy is finite for both stochastic and deterministic processes. The heat energy is used in breaking the hydrogen bonds which hold the molecules of liquid water together. The energy units should match so let's call entropy 0. Conservation of energy would allow: • ice getting colder and water getting hotter. gasping for air through the T. The element molar entropies are per mole of atoms so the oxygen value is for half a mole of oxygen molecules because oxygen exists as diatomic molecules. Entropy Budget of the Atmosphere Josg PINTO PEIXOTO, • ABRAHAM H. 7812,oxygen:0. eNotes plot summaries cover all the significant action of Entropy. Solution:. It is possible for a process to occur that lowers the energy of the system, but raises the entropy of the surroundings. ) How much of this entropy generation occurs within the iron ? (Sgen,int) c. Pressure: Atmospheric pressure at 1,01325 bar, i. The air can be modeled as an ideal gas and kinetic and potential energy effects are negligible. Thermodynamics Directory | Heat Transfer Directory. The energy processes that convert heat energy from available sources such as chemical fuels into mechanical work are the major concern of this science. Surroundings: the nearby air and any moisture or salt in the air plus any object in contact with the rusting iron. Entropy function. At standard pressure P o = 1 bar, the value is denoted as ΔS o vap and normally expressed in J mol −1 K −1. heating at constant volume and expansion at a constant temperature. Make it sacred. 35 MPa, 205 o C. OORT, 2 MARIO DE ALMEIDA, TM AND ANTONIO TOMI• • The balance equations for the entropy in the atmosphere are presented and discussed. Type: Full-length Release date: June 6th, 2006 Catalog ID: Dead 77 CD Label: Moribund Records Format: CD Reviews: 3 reviews (avg. The importance of total entropy change. Below this table is an image version for offline viewing. Ignore the energy carried away from the collision by sound. The entropy of the system never reduces. Conservation of energy would allow: • ice getting colder and water getting hotter. The second law of thermodynamics, or the law of increased entropy, says that over time, everything breaks down and tends towards disorder - entropy! Entropy is the amount of UNusable energy in any systems; that system could be the earth's environment or the universe itself. Realize when you're being reasonable and when you're being full of hot air. is augumented by 1·164 kJ kg −1 K −1, thermodynamic properties of Keenan et al. We then derive the entropy and chemical potential of an ideal gas and a condensate. Related Topics. One side contains air, the other side another gas, say argon, both regarded as ideal gases. Of course, there have been exceptions to this rule: Carl Jung was happy enough to think within a broad framework of ‘psychological thermodynamics’ and made the attempt to define stable personality traits (and the. Make it sacred. The second equation is a way to express the second law of thermodynamics in terms of entropy. (b) Calculate the entropy change (kJ/K) for the air. Compressed air energy storage (CAES), with its high reliability, economic feasibility, and low environmental impact. See Figure 3. The entropy of the reactants is 724. Bulk modulus elasticity: 1. Monday, We Need To Talk. If one assumes the atmosphere has a thickness $\mathrm{d}R$ then its volume is $\approx 4\pi R^2 \mathrm{d}R$. The differential heating of the atmosphere, resulting from surface heat ﬂuxes and tropospheric radiative cooling, corresponds to a net entropy sink. It is measured in joules of energy per unit kelvin. This is the project I submitted for the final year while reading for a B. The entropy of the air inside a balloon counts all the ways that the air molecules can be arranged while maintaining the same overall temperature, pressure, and volume. 0; Air is expanded from 2000 kPa and 500°C to 100 kPa and 50°C. iPad / iPhone Apple OS X. The moist entropy and related quantities ¾In analogy with the definition of k, we define the total specific entropy per unit mass of dry air as: s = sd + rsv + rLsL ¾sd, sv, and sL are the specific entropies of dry air, water vapour and liquid water, respectively. 4 The process involves no internal irreversibilities. For example, a stack of blocks falling over will result in a lower energy state and higher system entropy. However, you have to be sure that the ideal gas law can be used for that substance without major loss of accuracy, and you need to have an understanding of what specific heat is. 194 kJ of enthalpy per kg. 55 When a system undergoes a Carnot cycle, no entropy is produced within the system. The element molar entropies are per mole of atoms so the oxygen value is for half a mole of oxygen molecules because oxygen exists as diatomic molecules. A pointwise bound 3. Internal Energy, Enthalpy, & Specific Heat of Ideal Gases Instead of using tables to find a gases internal energy and enthalpy, the ideal gas equations could be used. 1, was designed by the writer several years ago. Entropy, as it relates to dynamical systems, is the rate of information production. The Clausius inequality forms the basis for the definition of a new property called entropy. Atrophy and Entropy, October 15, 2015 "The late afternoon air smells of yellow hay, the warm musk of manure, peppery fresh-cut grass, and chicken frying up nicely. However, rational and controllable synthesize of these intrinsically complex structures remains a challenge. As for annular flow. She wrested herself free, glared at her bag, pulled out a half filled book, a pen-in-well screwed tight, and walked out onto the deck. 3 μm in diameter) and saw the entropy decrease for periods lasting several tenths of a second. occurs without gain or loss. In this process, air undergoes isentropic (reversible adiabatic) expansion. 02479 m3 mol-1. Chapter 22 Heat Engines, Entropy, and the Second Law of Thermodynamics CHAPTER OUTLINE 22. 1004) as containing 'a whole world of the deepest thoughts and the most powerful feelings. Entropy and elliptic equations 1. " That very specific phrase, "in only one of which", is important because it is easy to infer that "the more. 0 kJ mol-1, and the entropy change of the system is -254 J K-1 mol-1. ) H 2 O(l) → H 2 O(g) ΔH = +44 kJ Solution The change in entropy of the surroundings after a chemical reaction at constant pressure and temperature can be expressed by the formula ΔS surr = -ΔH/T where ΔS surr is the change in entropy of the. SL: Use tables to calculate entropy changes. 2) dS = m Cp ln(T2 / T1) + m R ln(P1 / P2). The entropy change of the surroundings (per kilogram of air) is the heat transfer divided by the constant temperature of 293. In equation form, S 0. When a system moves from an ordered arrangement to a less order arrangement, the entropy of the system increases. The elemental entropy is defined by the following relation: $\mathrm{d}S=\frac{\mathrm{d}Q}{T},$ where dQ is the elemental exchanged heat and T denotes the thermodynamic temperature. A system with more random motion between molecules has greater entropy. This aspect might best be stated first as a simple example: In a room filled with air the individual molecules are moving at random and, because. Entropy and poker Here are two poker hands: Specifically, the entropy of a macrostate is equal to the natural logarithm of the number of microstates in that macrostate, times a number called Boltzmann's constant. ) On the other hand, the change in volume of a liquid is appreciably. 7B-3 : Entropy Change of an Isobaric Process: 6 pts: Consider a process in which 1. Entropy is positive anytime it makes a bigger mess or creates disorderly. Entropy decreases may occur in small systems over short time-scales. 2 Kozan Maru , 35°16'N, 126°03'E; and Kaba Maru and Hoei Maru. entropy [en´trŏ-pe] 1. 636 3 1026 3. Entropy of Mixing Last updated; Save as PDF Page ID 1945; The Mixing of Ideal Gases; References; Outside Links; Contributors; A gas will always flow into a newly available volume and does so because its molecules are rapidly bouncing off one another and hitting the walls of their container, readily moving into a new allowable space. In our solar system heat is generated everywhere including solar fusion and radiated heat from planets. where dq is a thermal energy input to the gas, du is a change in the internal energy of. Temperature After Mixing Of Gases - posted in Process Heat Transfer: Hello all! I want to calculate the temperature and pressure of mixed gases which are mixed at different temperature and pressure. where p is gas pressure, V is volume, is the number of moles, R is the universal gas constant (= 8. When the mixture is at equilibrium, determine the final temperature and pressure and the change in entropy of the mixture. Spontaneous Processes and Entropy •A spontaneous process is a physical or chemical change that occurs by itself. Standard absolute entropy values are given in units of joules per kelvin per mole; J K-1 mol-1; Values of standard absolute entropy (S°) for many substances have been tabulated. 1) (Aether/Gravity) FARMS FALSE GODS!!! Mutating Spider Deck (Aether/Entropy) Mutation of Serendipity (Entropy/Light). These being gases escape from the reaction and thus, entropy change is positive and reaction is thermodynamically favourable. If it took a billion years and a million different reactions doesn't matter. For example, a stack of blocks falling over will result in a lower energy state and higher system entropy. 4 °C, so this is an isothermal process. The specific heat of water is 4. Next we derive a consistent expression for the entropy of a mixture of dry air, wa-ter vapor, and either liquid water or ice. 0092,argon:0. Related Topics. 7–25 or 7–26 by employing the property relations for ideal gases (Fig. Entropy is a measure of the random activity in a system. Imagine that a group of molecules has ten units of energy. Scribd is the world's largest social reading and publishing site. Type: Full-length Release date: June 6th, 2006 Catalog ID: Dead 77 CD Label: Moribund Records Format: CD Reviews: 3 reviews (avg. py [filename] This shown below with the output: The closer the entropy value is to 8. Entropy, often denoted by the alphabet S, is a difference between sum of products and sum of reactants of a moles, generally used to the study of disorder & randomness of the different groups available due to chemical reaction of the moles. c^2 equation). 01 m 3 /kg, and compare the result to the value obtained by using the ideal gas equation of state. denotes a saturated vapor state. Bulk modulus elasticity: 1. What is Entropy? Perhaps there's no better way to understand entropy than to grasp the second law of thermodynamics, and vice versa. For example condensing mist in the air into one droplet organizes the mess and that would be negative entropy. Refer to the table below, or download the attachment. Based on this definition, we can distinguish the type of the reactive mixture: λ = 1. As for annular flow. The effects of variables such as air temperature, relative humidity, physical activity, and clothing on entropy generation are examined. If the constant-specific-heats assumption is valid, the above equation can be integrated and rearranged to. com Entropy is the general trend of the universe toward death and disorder. If directly reduced with carbon, C S 2 (liquid) is formed which remain in reaction mixture. You smoke till the world around you shrinks with every passing wisp. Heat flows from a hot object to a cold one. 4 kcal⋅mol −1 ⋅residue −1, is largely due to the loss of BB entropy. About the EPT open child menu. 4 per rotamer. What is the change in entropy of the water ?. The entropy of a substance increases with its molecular weight and complexity and with temperature. @Pat We can still make sense of (differential) entropy of delta functions; as intimated in the link in the question, it can be understood as the limiting entropy of a sequence of functions whose (compact) supports shrink to a point. Entropy is a measure of the number of ways a thermodynamic system can be arranged, commonly described as the "disorder" of a system. This applet calculates the thermodynamic properties of air given the pressure and entropy, pressure and density, specific energy and density, entropy and enthalpy, or pressure and temperature, in SI units (kg/m^3, J/kg, J/kg/K, m/s, Pa, K) or British Units (lb/ft^3, BTU/lbm, BTU/lbm/R, ft/s, psi, R). Entropy is a thermodynamic property, the value of entropy depends on the state of the system. Therefore, if pressure increases, a negative contribution is made on the change in entropy of an ideal gas, but depending on the change in temperature, the actual change in entropy for the system might be positive or negative. Calculate online thermodynamic properties of moist (humid) air based on Hyland and Wexler formulation approved by American Society of Heating, Refrigeration and Air-conditioning Engineers. The entropy of this system is large. Critical Point Data of Various Substances. 19 (NH 2) 2CO (s) ‐ urea ‐333. Since steam dryness has a significant effect on all these values, to enable greater heating efficiency it is crucial to supply steam that is as close to being 100% dry as possible. (b) Calculate the entropy change (kJ/K) for the air. , 2004); and (2) to favor solid solutions over intermetallic. By substituting du = C u d T and P = R T /u into Eq. 0403 kW/K Solution. Entropy Piano Tuner. Total enthalpy in air = air enthalpy + water vapor enthalpy = 30. The isentropic efficiency of a compressor or pump is defined as the ratio of the work input to an isentropic process , to the work input to the actual process between the same inlet and exit pressures. The Edge of Entropy Monday, December 13, 2010. The first law of thermodynamics, the conservation of energy, may be written in differential form as. For this problem, the change in entropy of the system is the sum of the changes in entropy of the air and oil, such that the entropy generation is then $$\sigma_{12} = \Delta S_{air,12} + \Delta S_{oil,12}$$ The basic property relations for entropy change of the air and oil are integrated assuming constant specific heats, to give. The irreversible entropy production by diffusion of water vapor for the whole atmosphere is. Air is heated in the lower cylinder using an external source. This on-line psychrometric calculator makes air property determination simple. 101 287ln 273. Assuming constant specific heats, determine the change in the specific entropy of air. Understanding the atom-sized machine involved both complicated calculations and observations. This is one example of a heat engine, which we study in this chapter. Monatomic Gas - Internal Energy. It follows from the second law of thermodynamics that the entropy of a system that is not isolated may decrease. 6 Entropy 22. The important properties for this discussion are: 1. 1 Entropy Change in Mixing of Two Ideal Gases. The phases of matter in order of increasing entropy are solid, liquid, then gas. entropy hypothesis where the entropy directly related to the number of authors. 3 Air is an ideal gas. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical. Entropy is a measure of randomness or disorder in a system. You exhale till there’s nothing left inside. Since pv= RT pv" = pivi" and Tv"- = Tiv"-then v (T. The QBME method characterizes the spatiotemporal dependence among the ambient air quality levels based on their location-specific quantiles and accounts for. Dystopian fiction is a post-Christian genre. 12 f ( wet bulb temperature, entropy of moist air, pressure ) 13 f ( wet bulb temperature, volume of moist air, pressure ) 14 f ( dew point temperature, relative humidity, pressure ) 15 f ( relative humidity, humidity ratio, pressure ) 16 f ( relative humidity, enthalpy of moist air, pressure ) 17 f ( relative humidity, entropy of moist air. A gas can be heated to the temperature of the bottom of the pond, and allowed to cool as it blows through a turbine. The approximate entropy is nearly unaffected by noise of magnitude below the filter level, r, and therefore robust to occasional very large or small artifacts. denotes a saturated liquid state. These lines extend at an angle from the saturated vapor line. UTK Award (10/01/2014 – 10/31/2014) * INVESTIGATOR TITLE SPONSOR AWARD; College of Arts and Sciences; McSween, Harry: Participation in DAWN Science Team: Regents of the Universi. Multi-elemental alloy nanoparticles (MEA-NPs) hold great promise for catalyst discovery in a virtually unlimited compositional space. Isentropic Expansion - Isentropic Compression for Ideal Gases. Of course, there have been exceptions to this rule: Carl Jung was happy enough to think within a broad framework of ‘psychological thermodynamics’ and made the attempt to define stable personality traits (and the. Entropy is a measure of the random activity in a system. It involves a comparison between the actual performance of a device and the performance that would be achieved under idealized circumstances for the same inlet and exit states. She longed for cool night air, but it was warm, and muggy. , the previous equation could be "integrated" easily. A diﬀerential form of Harnack’s inequality 3. First, they exploit the large thermal energy required to change a liquid to a vapor so we can remove lots of heat out of our air-conditioned space. Scribd is the world's largest social reading and publishing site. Vessel A contains air at 0. Search Search. Conservation of energy would allow: • ice getting colder and water getting hotter. If the constant-specific-heats assumption is valid, the above equation can be integrated and rearranged to. Note also that for substance AirH2O (psychrometrics), the specific entropy returned by this function is the entropy of the air and water vapor mixture per unit mass of dry air. When mined, it will drop 1-4 Perditio Vis Crystals (the number of crystals it will drop is countable by looking at the block). The second law of thermodynamics, or the law of increased entropy, says that over time, everything breaks down and tends towards disorder - entropy! Entropy is the amount of UNusable energy in any systems; that system could be the earth's environment or the universe itself. Anderson, there are a lot of sentences in the English language that contain the words "entropy" and "disorder," and most of them are wrong. If it took a billion years and a million different reactions doesn't matter. ENTROPY AND THE SECOND LAW OF THERMODYNAMICS ENTHALPY AND ENTROPY Consider this experiment: a drop of water is placed in a clean Petrie dish and the cover is put on. 82 Compare the entropy of the CO 2 molecules in the dry ice to the entropy of the CO 2 molecules in the inflated balloon. Spontaneous Processes and Entropy •A spontaneous process is a physical or chemical change that occurs by itself. It is a physical property of the substance. 8: Al 2 O 3 (s)-1675. Using the Steam Property Calculator, properties are determined using Inlet Pressure and the selected second parameter (Temperature, Specific Enthalpy, Specific Entropy, or Quality). The new cysteines spontaneously formed disulfide bonds on exposure to air in vitro. (At pressures below the triple-point pressure of 518 kPa, carbon dioxide exists as a solid or gas. You try to take in the world one step at a time, but you were always an ‘all or nothing’ kinda person, so you just go ahead and gobble it up. In the example of air density the entropy in the corner of the room that initially had all the air decreases as the air expands, but the total entropy in the room increases. If you require a reliable source of thermodynamic properties, we recommend you obtain a copy of EES (Engineering Equation Solver) from fchart. Entropy, as it relates to dynamical systems, is the rate of information production. activestate. Next we derive a consistent expression for the entropy of a mixture of dry air, wa-ter vapor, and either liquid water or ice. 2 bar, 600C. 15 288 s2 =1005ln − = After compression 53 0. According to Wikipedia, the entropy is: $$\frac1 2 \log_2 \big( 2\pi e\, np(1-p) \big) + O \left( \frac{1}{n} \right)$$ As of now, my every attempt has been futile so I would be extremely appreciative if someone could guide me or provide some hints for the computation. The Entropy Of Dry Air At A Given Constant Pressure? - posted in Industrial Professionals: hi, how do you calculate the entropy of air at a given pressure? this is to help me to plot my gas turbine cycle on excel Many thanks d. PBMs or PB2Ys on sweeps off west coast of Korea sink Japanese cargo ships Tatsuchiyo Maru , 34°00'N, 126°00'E; No. sda = specific entropy of dry air, kJ/(kg·K) (dry air). It follows from the second law of thermodynamics that the entropy of a system that is not isolated may decrease. Measuring entropy: Scanning-tunneling microscope gives glimpse of the mysterious property Date: February 14, 2017 Source: Penn State Summary: The scanning-tunneling microscope (STM), which is used. Entropy and Light Wednesday, July 18, 2012 The blog will stay here, until entropy eventually claims it too, is the plan. Critical temperature: 132. This is the project I submitted for the final year while reading for a B. These are often heads of departments, deans, people funding the research, directors of laboratories, senior scientists close to retirement, etc. 158 3 1026 8. 0403 kW/K Solution. thermal conductivity. Conservation of energy would allow: • ice getting colder and water getting hotter. , Steam (or Water), Nitrogen, R12, CarbonDioxide, Methane, etc. dS > q/T for a natural change. Entropy is positive anytime it makes a bigger mess or creates disorderly. Such a state has a much greater entropy, and so is much more likely to occur. These were Lisette’s favorite days of the year. 93: Ambrose, Sprake, et al. The air, as we crossed the Ventura County line, became putrid with smoke. 3 Air is an ideal gas. In the ideal process it can remain remain constant, but in actual process the entropy of system and universe always increases. Entropy is the measure of the disorder of a system. Therefore its heat capacity at close to normal temperatures and pressures may with good accuracy be taken equal to. The ambient air temperature is constant at 20. The entropy of mixing to make 1 mol of air from its constituent elements is to be calculated. According to Wikipedia, the entropy is: $$\frac1 2 \log_2 \big( 2\pi e\, np(1-p) \big) + O \left( \frac{1}{n} \right)$$ As of now, my every attempt has been futile so I would be extremely appreciative if someone could guide me or provide some hints for the computation. 15 288 s2 =1005ln − = After compression 53 0. Entropy in my system occurs at only one point in the rotation of the flywheel. Some tacit assumptions regarding their correlation have been shown to be wrong. Entropy of Mixing Last updated; Save as PDF Page ID 1945; The Mixing of Ideal Gases; References; Outside Links; Contributors; A gas will always flow into a newly available volume and does so because its molecules are rapidly bouncing off one another and hitting the walls of their container, readily moving into a new allowable space. Jeff Phillips gives a crash course on entropy. Second , entropy is the measure of energy dispersal, as a function of temperature. The entropy of mixing to make 1 mol of air from its constituent elements is to be calculated. The second law tells us that entropy, which is a measure of disorder, always increases; most of the energy exerted in any process is unavailable for work because it’s wasted as heat. The Relationship of Entropy to Temperature The definition of temperature in terms of molecular kinetic energy, the "kinetic temperature", is commonly used in introductory treatments of thermodynamics. Note also that for substance AirH2O (psychrometrics), the specific entropy returned by this function is the entropy of the air and water vapor mixture per unit mass of dry air. Assuming constant specific heats, determine the change in the specific entropy of air. Determine the rate of entropy change of the air. 20 and tabulated thermodynamic parameters (the heat capacities of S α and S β, ΔH fus (α), and the. 948 PROPERTY TABLES AND CHARTS TABLE A-9 Properties of air at 1 atm pressure Specific Thermal Thermal Dynamic Kinematic Prandtl Temp. 632 Heat Engines, Entropy, and the Second Law of Thermodynamics Q22. Identify appropriate system or systems on the sketch provided, show mass/energy interactions (EFD), list any assumptions and basic equations, and provide your. When the gas in vessel B is heated, it expands against the movable piston and does work \ (dW = pdV\). The internal energy and enthalpy of ideal gases depends only on temperature, not on volume or pressure. A positive result means the entropy of the reaction increased meaning the products were more disordered than the reactants. Entropy Balance for Closed Systems - The entropy change of a closed system during a process is equal to the sum of the entropy transferred through the system boundary by heat transfer and the entropy generated within the system boundaries as a result of irreversibilities. Calculate the entropy change of the air. It follows from the second law of thermodynamics that the entropy of a system that is not isolated may decrease. In the example of air density the entropy in the corner of the room that initially had all the air decreases as the air expands, but the total entropy in the room increases. The degree of order or disorder in a system may be described in terms of the probability or improbability of the observed state. Heat is transferred from the air until the pressure reaches 120 kPa. The second law of thermodynamics is acting on the universe, but don't worry, it will be a very, very long time before it achieves complete entropy. Entropy is positive anytime it makes a bigger mess or creates disorderly. Enthalpy Entropy (h-s) or Mollier Diagram. It is inescapable, and even if we try to ignore it, the result is a collapse of some sort. ENTROPY AND THE SECOND LAW OF THERMODYNAMICS ENTHALPY AND ENTROPY Consider this experiment: a drop of water is placed in a clean Petrie dish and the cover is put on. Thermodynamics is a branch of physics that deals with heat and temperature, and their relation to energy, work, radiation, and properties of matter. 3 μm in diameter) and saw the entropy decrease for periods lasting several tenths of a second. In energy, it marches to thermodynamic equilibrium; in Information Theory, it marches to purity. 71 kJ/mol or about 2,260 kJ/kg water. The basic operating principle behind Compressed Air Energy Storage (CAES) is extremely simple. In Table 2 , sda has been assigned a value of 0 at 0°C and standard atmospheric pres-sure. (Refer p-V and T-s diagrams above). As can be seen in the equation above, for an internally reversible process the cyclic integral of δQ / T is zero. The entropy of a substance increases with its molecular weight and complexity and with temperature. Or in any critical application as the calculator could disappear at any time. The heat expelled from the room (the system), involved in the operation of the air conditioner, will always make a bigger contribution to the entropy of the environment than will the decrease of the entropy of the air of that system. However, you have to be sure that the ideal gas law can be used for that substance without major loss of accuracy, and you need to have an understanding of what specific heat is. ” That very specific phrase, “in only one of which”, is important because it is easy to infer that “the more. It is sometimes known as the h-s diagram and has an entirely different shape from the T-s diagrams. In countries where the metric system is more common, m3/min or m3/h is sometimes being used, but even there, CFM is the most common unit. Example: The air at T=288K and standard atmosphere is compress to P=5 times of standard atmosphere pressure with a temperature 456. The entropy measures the heat divided by the absolute temperature of a body. Calculate online thermodynamic properties of moist (humid) air based on Hyland and Wexler formulation approved by American Society of Heating, Refrigeration and Air-conditioning Engineers. 2) dS = m Cp ln(T2 / T1) + m R ln(P1 / P2). 4 The process involves no internal irreversibilities. The standard molar entropy of water is 69. (Entropy) 16. For instance, densely and sparsely grafted nanoparticles show distinct dispersion and assembly behaviors within polymer matrices due to the entropy variation associated with conformational changes in brush and matrix chains. The entropy of mixing to make 1 mol of air from its constituent elements is to be calculated. Then the air conditioning goes off, and the temperature in the room begins to converge on the temperature outside. 8° in E-plane, 15. Entropy is negative anytime it cleans up a mess. 6 J/K, the entropy of the products is 174. VANCE AIR FORCE BASE, Okla. Second , entropy is the measure of energy dispersal, as a function of temperature. (d) Determine the entropy generation for the entire process (both air and water). We can even see remnants of this idea manifest in our modern concept of ghosts, which are often depicted as anthropomorphic clouds or semi-transparent vapors [28]. I assume that if you read further, you understand partial derivatives, cross-derivatives, and the integral of #1/x#. Claude Shannon introduced this expression for use in information theory , but similar formulas can be found as far back as the work of Ludwig Boltzmann and J. Entropy noise aﬀects the thermoacoustic stability of the combustor. Additionally, any device with. Entropy is an important mental model because it applies to every part of our lives. If the central drama of the age of faith was the conflict between salvation and damnation by deity, in our secular modern age this drama has been transposed to a conflict between humanity’s salvation or damnation by society in the historical arena. Air is compressed in a piston?cylinder device from 90 kPa and 20{eq}^{\circ} {/eq}C to 600 kPa in a reversible isothermal process. The modern version of the second law of thermodynamics can be stated in numerous ways. Shannon in the paper „ A Mathematical Theory of. Entropy and the Second Law of Thermodynamics That direction is set by a quantity called entropy Only one of these scenarios happens, so something must be controlling the direction of energy flow. But, as and when we approach this simple theory, it starts becoming more complex because of the thermodynamics involved. Scribd is the world's largest social reading and publishing site. Entropy is an important mental model because it applies to every part of our lives. Jeff Phillips gives a crash course on entropy. Or both for that matter. Malignant Cell Harvest (Air/Death) Mandelbrot's Dragons (Air, splash Aether) (Unupgraded. The moist entropy and related quantities ¾In analogy with the definition of k, we define the total specific entropy per unit mass of dry air as: s = sd + rsv + rLsL ¾sd, sv, and sL are the specific entropies of dry air, water vapour and liquid water, respectively. 5 percent can have adverse physiological effects, and atmospheres with less than 16 percent oxygen can become life threatening. By work I generally mean move something; useful work might be turning a drive shaft, for example, as opposed to waste heat that cannot. PBMs or PB2Ys on sweeps off west coast of Korea sink Japanese cargo ships Tatsuchiyo Maru , 34°00'N, 126°00'E; No. Example:- Ice melts at 0 0 C with latent heat of fusion= 339. The laws of thermodynamics do not particularly concern themselves with the specific how and why of heat transfer, which makes sense for laws that were formulated before the atomic theory was fully adopted. The heat expelled from the room (the system), which the air conditioner transports and discharges to the outside air, always makes a bigger contribution to the entropy of the environment than the decrease of the entropy of the air. Temperature profiles show that the driving force ΔT or 1/ΔT is more uniformly distributed in the countercurrent than in the cocurrent flow operation. Entropy is negative anytime it cleans up a mess. If one assumes the atmosphere has a thickness $\mathrm{d}R$ then its volume is $\approx 4\pi R^2 \mathrm{d}R$. Calculations of entropy fluxes and production rate have been evaluated with some success to study atmospheric processes. Harnack’s inequality B. Some patterns emerge when these values are compared. For an ideal gas it. 632 Heat Engines, Entropy, and the Second Law of Thermodynamics Q22. For a pure component, Δ S v consists of translational, rotational, and conformational motion of molecules. Based on this definition, we can distinguish the type of the reactive mixture: λ = 1. 7812,oxygen:0. It allows 21 different combinations of input variables to be used for calculations. 3 μm in diameter) and saw the entropy decrease for periods lasting several tenths of a second. Entropy can be thought of as a measure of "wasted" energy, that is, energy that cannot be converted to useful work. 101 287ln 273. Entropy is positive anytime it makes a bigger mess or creates disorderly. 01 m 3 /kg, and compare the result to the value obtained by using the ideal gas equation of state. Air is now heated for 15 min by a 200-W resistance heater placed inside the cylinder. The total entropy, S 1 = ∑n i (C v ln T + R ln V i + S i)1 Note the term S i. AbstractThe effect of 1 at. PROPERTIES OF HELIUM CONTENTS A. 7 MPa, 95 o C while vessel B contains air at 0. Compressed air energy storage (CAES), with its high reliability, economic feasibility, and low environmental impact. Calculate the increase of entropy in a system with reversible and irreversible processes. Human entropy is good entropy, but it takes a long time to get 512 bytes’ worth. 10 −6 kg/ (s m) = MPa s. (d) Determine the entropy generation for the entire process (both air and water). Assuming constant specific heats, determine the change in the specific entropy of air. So go ahead wander into the kitchen to get yourself a cold one. 334 Chapter 6 Using Entropy – evaluating isentropic efficiencies for turbines, nozzles, com-pressors, and pumps from Eqs. Substituting for the definition of work for a gas. Entropy is a measure of the random activity in a system. What change in entropy occurs when a 27. Standard absolute entropy values are given in units of joules per kelvin per mole; J K-1 mol-1; Values of standard absolute entropy (S°) for many substances have been tabulated. C against about 1 kJ/kg. Increasing the entropy of the system comes naturally. Developers assume no liability and are not responsible for any misuse or damage caused by this program. Therefore, if pressure increases, a negative contribution is made on the change in entropy of an ideal gas, but depending on the change in temperature, the actual change in entropy for the system might be positive or negative. Boltzmann and Clausius' experiential research led to the revolutionary concept that everything in nature tends to flow from order to disorder, and. The following theorem is the main tool which allows to compute h(T). This concept is fundamental to physics and chemistry, and is used in the Second law of thermodynamics, which states that the entropy of a closed system (meaning it doesn't exchange matter or energy with its surroundings) may never decrease. Let n i be the number of moles of each gas and V i is the volume it occupies. The Entropy Crystal is a glowing ore added by Thaumcraft 6. Malignant Cell Harvest (Air/Death) Mandelbrot's Dragons (Air, splash Aether) (Unupgraded. Yi Cui’s team at Stanford University, California, extract energy with 74 per cent efficiency using manganese dioxide nanorods and silver electrodes 1. denotes a saturated liquid state. If you can't back it. It is a physical property of the substance. Left huffing, and her heart pounding faster than from a cursed dream. The function s° represents only the temperature- dependent part of entropy. Some tacit assumptions regarding their correlation have been shown to be wrong. Revised air quality index derived from an entropy function. Truly understanding entropy leads to a radical change in the way we see the world. Mollier Diagram. Aluminum: Al(s) 0: 28. Question: Air is expanded from 200 psia and 500{eq}^{\circ} {/eq}F to 100 psia and 50{eq}^{\circ} {/eq}F. 10 −6 kg/ (s m) = MPa s. some of it is lost as heat energy to the surrounding air, increasing entropy. Four different disulfide bridges (linking positions 9-164, 21-142, 90-122, and 127-154) were introduced into a cysteine-free phage T4 lysozyme at sites suggested by theoretical calculations and computer modeling. 2) dS = m Cp ln(T2 / T1) + m R ln(P1 / P2). USAAF B-24s (13th Air Force) bomb Japanese shipping and shore installations at Makassar, sinking gunboat Kenzan Maru and cargo ship Hakko Maru, 05°08'S, 119°35'E. 1100 kJ/mol K = 3. Some scientific and engineering data online german. The internal energy is the total of all the energy associated with the motion of the atoms or molecules in the system. The second equation is a way to express the second law of thermodynamics in terms of entropy. Therefore its heat capacity at close to normal temperatures and pressures may with good accuracy be taken equal to. Second , entropy is the measure of energy dispersal, as a function of temperature. Let the anxious contract you’ve unwittingly written evolve slowly and uncomfortably into a relationship. Compare your result with that using the s o functions in Table 5s and with that assuming a constant specific heat evaluated from Table 5s at 25 °C. Vladimir’s Blues (Jlin Remix) 17. The enthalpy, specific heat and entropy of this study are also in full agreement with those of the NBS table and Vargaftik's table (1975) for real gas air. (a) What is the entropy change of the universe?. If you can't back it. Build an impenetrable bastion upon that ground. 4 °C, so this is an isothermal process. The entropy of a substance increases with its molecular weight and complexity and with temperature. These lines extend at an angle from the saturated vapor line. In order to help me keep track of what each doll needs, I'm putting together a TDL for each group. This aspect might best be stated first as a simple example: In a room filled with air the individual molecules are moving at random and, because. Enthalpy-Entropy Diagram (Air) - Free download as PDF File (. Also, the freezing-point temperature of carbon dioxide is the triple-point temperature of 56. It deals with. 12 f ( wet bulb temperature, entropy of moist air, pressure ) 13 f ( wet bulb temperature, volume of moist air, pressure ) 14 f ( dew point temperature, relative humidity, pressure ) 15 f ( relative humidity, humidity ratio, pressure ) 16 f ( relative humidity, enthalpy of moist air, pressure ) 17 f ( relative humidity, entropy of moist air. INTRODUCTION. The standard absolute entropy of a substance, S°, is the absolute entropy of a substance in its standard state (298. Iconography (Konx-Om-Pax Remix). 48, respectively, including for ideal gases the appropriate use of Eqs. Let n i be the number of moles of each gas and V i is the volume it occupies. Due to the force of gravity, density and pressure do not even out vertically. 40 103-kg cars both traveling at 16. For entropy wave advection, the main outstanding challenges pertain to the effect of real combustor hydrodynamic flow features on the advection process: these have not yet been considered in any detail. The air can be modeled as an ideal gas and kinetic and potential energy effects are negligible. Critical Point Data of Various Substances. Air is heated in the lower cylinder using an external source. 52863609x10-2 0. Entropy cannot be destroyed (consumed), only generated and transferred from one system to another (in an isolated system, entropy can only increase). Critical temperature: 132. Description. Specific Heat Capacities of Air. ) On the other hand, the change in volume of a liquid is appreciably. 292 kJ/K (B) −0. These were Lisette’s favorite days of the year. 1) To find the change in entropy in this case, we have to use twin energy equation for pressure. Entropy comes from the second law of thermodynamics, which states that all systems tend to reach a state of equilibrium. 02479 m3 mol-1. Thermophysical properties of air: Boiling temperature (at 1 bara): 78. So when we have a house full of air, we can expect the molecules to distribute themselves pretty evenly throughout. Because it is an isothermal process, i. download the script: Entropy change of ideal gases Recall that entropy, which is defined as δq rev /T, is a property of state. It is the end user's responsibility to obey all applicable local, state, federal, and international laws. Therefore, if pressure increases, a negative contribution is made on the change in entropy of an ideal gas, but depending on the change in temperature, the actual change in entropy for the system might be positive or negative. The N99 protective mask is a basic type of mask which helps in protecting the users from around 99% of airborne particulates (PM 2. Even though the moist air is cooler than the separated water and dry air, the moist air contains more thermal energy. The matter and its environment relevant to a particular case of energy transfer are classified as a system, and everything outside of that system is called the surroundings. 01 m 3 /kg, and compare the result to the value obtained by using the ideal gas equation of state. The chart contains a series of constant. $\begingroup$ I found several formulas for entropy but there is no such thing as (Cpa - R), usually only Cpa Also you see, for different states the air and vapor can be in different proportions, so if the reference point is different then there will be errors, I think. (8 SEMESTER) ELECTRONICS AND COMMUNICATION ENGINEERING CURRICU. But in doing so, we inevitably increase entropy elsewhere, so the overall balance is positive. Note that the heat transfer to the surroundings is the negative of the heat transfer to the nozzle: qsurround = 3. Two kilograms of air are stored in a rigid volume of 2 m3 with the temperature initially at 300°C. sas = ss − sda, difference between specific en tropy of moist air at satu-ration and that of dry air itself, kJ/(kg·K) (dry air), at same pres-sure and temperature. entropy [en´trŏ-pe] 1. 20 and tabulated thermodynamic parameters (the heat capacities of S α and S β, ΔH fus (α), and the. The computational. 293kg/m3 (2018/6/2 16:58:52). 0092,argon:0. Recently, Mr. (c) Find the entropy change (kJ/K) for the water. It is a reversible adiabatic process. What hap-pens and and what are the causes? The system is the Petri dish and its contents. % Si addition to the refractory high-entropy alloy (HEA) Ta–Mo–Cr–Ti–Al on the high temperature oxidation resistance in air between 900 °C and 1100 °C was studied. Edison, NJ -- -- 05/04/2020 -- A new market study is released on Global Automotive Over-The-Air (OTA) Market with data Tables for historical. Air is expanded from 2000 kPa and 500C to 100kPa and 50C. Enthalpy Entropy (h-s) or Mollier Diagram. 3144 j/ ( o K mole)), and T is the absolute temperature. py that can be run from the shell command line by with the following command: python file_entropy. I did commit one faux pas, that I bought a set of professionally made PAPR hoods from Zoro. This is the reason that in our known universe, entropy s is always positive. Standard Thermodynamic Values at 25°C Please note that enthalpy and free energy values are given in kJ/mol while entropy values are given in J/(mol·K). (Regardless, the entropy of the universe is ≥ 0. • Examples include: A rock at the top of a hill rolls down. Find the change in entropy of the surrounding air resulting from the collision if the air temperature is 21°C. This applet calculates the thermodynamic properties of air given the pressure and entropy, pressure and density, specific energy and density, entropy and enthalpy, or pressure and temperature, in SI units (kg/m^3, J/kg, J/kg/K, m/s, Pa, K) or British Units (lb/ft^3, BTU/lbm, BTU/lbm/R, ft/s, psi, R). Thus Using the equation of state for an ideal gas ( ),. A moist entropy potential temperature -- denoted by $θ_{s}$ -- is defined analytically in terms of the specific entropy for moist air. Made by faculty at the University of Colorado Boulder, Department of Chemical & Biological. Properties Value Units Auto ignition temperature [3,a] 500-585 °C 932-1085 °F…. 46 kg of air initially at 275 kPa and having a specific volume of 0. com or REFPROP from NIST. 0, the higher the entropy. The variation of entropy with pressure is accounted for by the last term in Eq. Abstract This paper addresses an equation for moist entropy in the framework of cloud-resolving models. are talking about is so unimaginably high, probabilistic entropy laws concerning diffusion always provide us with accurate results. Calculation of thermodynamic state variables of air. entropy of moist air, pressure ) 18 f ( relative humidity, volume of moist air, pressure ). occurs without gain or loss. The enthalpy of moist air, in kJ/kg, is therefore: h = (1. This is one example of a heat engine, which we study in this chapter. Ignorance of it is responsible for many of our biggest mistakes and failures. Though it was released early in '08, it came to my attention this summer and sank its hooks into me immediately with its West. To recover entropy, you have to consider a sequence of dice throws, and ask how many questions per roll you need in an optimal strategy, in the limit that the number of rolls goes to infinity. Calculate the standard molar entropy changes for the solid ↔ liquid and liquid ↔ vapor transitions for. 3: Aqueous Solutions: Ca 2+ (aq)-542. If the entropy of Keenan et al. The following theorem is the main tool which allows to compute h(T). The N99 protective mask is a basic type of mask which helps in protecting the users from around 99% of airborne particulates (PM 2. A suitable integration will enable you to solve the entropy change for a fluid process. 82 Compare the entropy of the CO 2 molecules in the dry ice to the entropy of the CO 2 molecules in the inflated balloon. In energy, it marches to thermodynamic equilibrium; in Information Theory, it marches to purity. Entropy and Light Wednesday, July 18, 2012 The blog will stay here, until entropy eventually claims it too, is the plan. The air in this example has 55. As this happens, the air expands and pushes against a piston, causing it to move. Entropy Budget of the Atmosphere Josg PINTO PEIXOTO, • ABRAHAM H. 14866252x10-6. 2 Kinetic and potential energy changes are negligible. Here and now is all that matters in entropy measurements. Solved Problem 6. Im getting lost at the entropy part of a, I know my m air which is 11. The "Gas Tables Calculator" calculates caloric properties of moist air and undissociated combustion gases from 200 K up to 3300 K. 15 K for the surroundings. Condensation temperature (at 1 bara): 81. Derives equations to calculate entropy changes for an ideal gas as temperature and pressure changes. 0, the higher the entropy. In chemistry, the kind of energy that entropy measures is motional energy — of molecules that are translating (moving and colliding), rotating, and vibrating (atoms in a molecule moving as though the bonds were springs) — and phase change energy (enthalpy of fusion or vaporization). (A) Find the efficiency of the engine.


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# Two cells of equal  and of internal resistance  and  are connected in series. On connecting this combination to an external resistance  it is observed that the potential difference across the first cell becomes zero. The value of  will be a) b) c) d)

## Question ID - 150373 :- Two cells of equal  and of internal resistance  and  are connected in series. On connecting this combination to an external resistance  it is observed that the potential difference across the first cell becomes zero. The value of  will be a) b) c) d)

3537

(b)

Let the voltage across any one cell is  then

But

Next Question :
 Radiowaves of constant amplitude can be generated with a) FET b) Filter c) Rectifier d) Oscillator

format: plain


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## Precalculus (6th Edition)

sample: $(1999,35)$ $(2001,29)$ $(2003,22)$
Each row represents an ordered pair: $(1999,35)$ $(2001,29)$ $(2003,22)$ $(2005,23)$ $(2007,20)$ $(2009,20)$


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# Stop Internet Warming! [closed]

Write a program that will output another distinct program, and so on, while using as few distinct characters (and as few bytes) as possible.

For example, program 1 should output program 2, and when program 2 is executed, it should output program 3. This can be nested as deeply as needed, but must be at least 3 distinct programs deep.

## Rules

• Your program can take no input.

• When the program is executed, the output should be the source of another, different program. This includes the STDERR stream. This can continue as many times as needed, but must occur at least three times.

• The output source code may be in a separate language.

## Example

$<program-1> <program-2>$ <program-2>
<program-3>

$<program-3> <empty>  ## Scoring Each answer is scored by the following formula: (length_in_bytes * number_of_distinct_characters) / number_of_distinct_programs  For example, if your answer was 10 bytes long, contained 5 distinct characters, and output 3 distinct programs, your score would be: (10 * 5) / 3  or 16.66. Lowest score wins. Note: This challenge was inspired by the comments on this StackOverflow question. ## closed as too broad by jimmy23013, Mego♦, Stewie Griffin, Addison Crump, TanMathJan 14 '16 at 8:36 Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question. • I suggest you add "lowest score wins" and remove anything above the TL;DR as per this meta answer – agtoever Jan 14 '16 at 8:09 • I'm voting to close as too broad because there is no criteria on what the programs should do, other than spitting out other programs. It would be trivial to create an infinite sequence of programs in stack-based languages with implicit output like Seriously. – Mego Jan 14 '16 at 8:10 • What's the score if you create infinite programs? 0? – agtoever Jan 14 '16 at 8:11 • For example: Q;+ will result in an infinite sequence of Seriously programs, each containing the previous program repeated twice. Score: 3*3/infinity – Mego Jan 14 '16 at 8:15 ## 2 Answers # Vitsy, 8 bytes, 8 distinct character, ∞ programs (score 0) This is a simple proof in another stack-based language of Mego's comment. 'Drd3*Z1 ' rd3*Z Standard quine formula D 1 Increase the number of ones every output (output 1 will have 11, 2: 111, 3: 1111, etc.) # Perl 5 - 34 bytes, 19 distinct characters, 10000000 programs (score 0.0000646) $p="print q{$p}"for 1..1e7;print$p

The score can be lowered arbitrarily by increasing the constant 1e7, at the expense of taking longer and producing larger programs.


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## Search Result

### Search Conditions

Years
All Years
for journal 'PTP'
author 'V.* P.* Seth' : 7
total : 7

### Search Results : 7 articles were found.

1. Progress of Theoretical Physics Vol. 40 No. 1 (1968) pp. 187-188 : (5)
Use of Factorization in Constructing Superconvergent Sum Rule
V. P. Seth and B. K. Agarwal
2. Progress of Theoretical Physics Vol. 41 No. 3 (1969) pp. 847-848 : (5)
Superconvergence Sumrules for $\rho\Sigma$ and $\rho\Xi$ Elastic Scattering
V. P. Seth and B. K. Agarwal
3. Progress of Theoretical Physics Vol. 41 No. 3 (1969) pp. 852-853 : (5)
Construction and Testing of Superconvergent Sum Rules for a Linear Combination of Products of Amplitudes
M. C. Sharma, V. P. Seth and B. K. Agarwal
4. Progress of Theoretical Physics Vol. 42 No. 2 (1969) pp. 411-413 : (5)
A Comment on the $u = 0$ Superconvergent Sum Rule for ${\pi}N$ Scattering
B. K. Agarwal, V. P. Seth and M. C. Sharma
5. Progress of Theoretical Physics Vol. 44 No. 2 (1970) pp. 432-436 : (5)
Exotic Exchange State and New Sum Rules
V. P. Seth
6. Progress of Theoretical Physics Vol. 45 No. 4 (1971) pp. 1139-1142 : (5)
Duality Diagrams and Sum Rules
V. P. Seth
7. Progress of Theoretical Physics Vol. 47 No. 5 (1972) pp. 1774-1776 : (2)
A Comment on the Backward $K^-n \to \Lambda \pi ^-$ Scattering
V. P. Seth


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# Deletion residuals

Please can you help me to solve this problem. It should be calculated by vectorization. The question is:

The i-th deletion residual $e_{(-i)}$ is defined as $e_{(-i)} = y_i - X^\top B_{(-i)}$
where $(X^\top)$ is the i-th row of the design matrix $X$ and $B_{(-i)}$ is a column vector of least square parameter estimates calculated without the i-th observation. Write some annotated R code to calculate the deletion residuals when the linear model $y_i = B_0 + B_1 X_i + B_2X_i^2 + E_i$
is fitted to the data in the file quadratic.txt. By drawing suitable plot, comment on the distribution of these deletion residuals.

Edit

I wrote some r codes , but it just gives me residual. I want to calculate deletion residual for i-th cases.

> quad<-read.table("quadratic.txt", header=T)

tha data is like this

x=(0.75078002, 0.70959645 ,0.07482854,0.60755927 ,0.55037327 ,0.55037327,
0.35458257 ,0.21994714,0.66369585,0.12381099, 0.12381099,0.12381099,
0.77869635,0.63917962)

and

y=(18.715191,17.394049,-2.346149,5.528978,6.765831,6.324425,13.803874,
15.007047,4.034973,12.383765,14.823395)

1          2          3          4          5          6          7
3.7933593  3.2646946 -4.9080046 -6.6589585 -4.3477835 -1.1856694  8.7046506
8          9         10         11
1.7549092  0.6237708 -3.0781575  2.0371889

-

## locked by chl♦Dec 20 '12 at 20:41

This post has been locked while disputes about its content are being resolved. For more info visit meta.

Since this is homework, can you explain what work you've done so far or what part of the problem is giving you trouble? We prefer not to just solve your homework for you, since then you don't learn very much... –  Jonathan Christensen Dec 1 '12 at 23:43
I added the 'homework' tag, but you should feel free to explain how this arises in a way that doesn't come under the tag if you think it doesn't belong. –  Glen_b Dec 2 '12 at 1:12
you can get studentized deleted residuals via rstudent or MASS::stdres (?rstudent or ?MASS::stdres to see the help on them) - if you want raw deleted residuals you'd need to compute them directly or from the standardized versions –  Glen_b Dec 2 '12 at 16:12
This question should not be responded to, this is an assigned question in a degree programme. –  VVV Dec 15 '12 at 16:27
@nina If there is a serious problem with this question, please flag it for deletion instead of replacing it by $11111111111...$ These changes can be rolledback, anyway. –  user10525 Dec 20 '12 at 20:29

This kind of jackknifing problem can be programmed straightforwardly, but that usually results in a tangle of for loops. Some linear algebraic manipulations go a long way in drastically reducing code length (if your computer's memory can handle it).

• Consider the original regression equation $$Y_i= \boldsymbol{X}_i'\boldsymbol{\beta} + \varepsilon_i;\;i=1, \ldots, n$$ where $\boldsymbol{X}_i$ is a $k\times 1$ vector of regressors.You can write this more compactly as $$\boldsymbol{Y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\varepsilon}$$

• Then the model that you want to estimate can be stacked up as $$\begin{bmatrix} \boldsymbol{Y}^{(-1)} \\ \vdots \\ \boldsymbol{Y}^{(-n)} \\ \end{bmatrix} = \begin{bmatrix} \mathbf{X}^{(-1)} & & \\ & \ddots & \\ & & \mathbf{X}^{(-n)} \end{bmatrix} \underbrace{\begin{bmatrix} \boldsymbol{\beta}^{(-1)} \\ \vdots \\ \boldsymbol{\beta}^{(-n)} \\ \end{bmatrix}}_{\equiv \boldsymbol{\beta}^-} + \begin{bmatrix} \boldsymbol{\varepsilon}^{(-1)} \\ \vdots \\ \boldsymbol{\varepsilon}^{(-n)} \\ \end{bmatrix}$$ where $\boldsymbol{Y}^{(-i)} = [Y_1, \ldots, Y_{i-1}, Y_{i+1}, \ldots, Y_n]'$ is the $n-1 \times 1$ vector with the $i$-th row (of $\boldsymbol{Y}$) deleted; and $\mathbf{X}^{(-i)} = [\boldsymbol{X}_1, \ldots, \boldsymbol{X}_{i-1}, \boldsymbol{X}_{i+1}, \ldots, \boldsymbol{X}_n]'$ is the $(n-1)\times k$ matrix with the $i$-th row (of $\mathbf{X}$) deleted. Note that the design matrix in this regression equation is block diagonal. Also, this is a very large system.

• Once $\widehat{\boldsymbol{\beta}}^-$ in the system above is estimated (by least squares), the residuals you want to estimate ($Y_i - \boldsymbol{X}_i'\widehat{\boldsymbol{\beta}}^{(-i)}$) can be had simply as $\boldsymbol{Y} - \mathrm{diag}(\mathbf{X}\mathrm{ivec}(\widehat{\boldsymbol{\beta}}^-))$, where the $\mathrm{diag}$ operator extracts the diagonal and $\mathrm{ivec}$ is the inverse of the $\mathrm{vec}$ operator which stacks the columns of the matrix.

## R code

Here is some R code to show how this can be done. The only trick here is constructing the stacked, row-deleted matrices, and then you are left with one (very) large least squares problem to solve.

iN <- 50                # number of observations
iK <- 4                 # number of regressors (including constant)

mX <- matrix(rnorm(iN*iK), nrow = iN, ncol = iK)  # design matrix
vBeta <- c(1, 2, 3, 4)                            # coefficients
vY <- mX%*%vBeta + matrix(rnorm(iN))              # dependent variable
mXStacked <- (diag(iN)%x%mX)[-seq(from = 1,
to = iN*iN, by = iN+1), ]  # Stacked design matrix
vYStacked <- vec(vY%*%t(rep(1, iN)))[-seq(from = 1,
to = iN*iN, by = iN+1), ]   # Stacked outcomes
vBetaMinus <- solve(t(mXStacked)%*% mXStacked,
t(mXStacked)%*%vYStacked)           # estimated coefficients
mBetaMinus <- matrix(vBetaMinus, nrow = iK, ncol = iN)
vResid <- vY - diag(mX%*%mBetaMinus)                  # required residuals

matplot(vResid, type = "l")           # plot the estimated residuals

### Given dataset

The above R code can be easily adapted to the given dataset. Your outcome vector appears to be shorter than the regressor vector, so I have clipped off some of the latter.

vY <- as.matrix(c(18.715191,17.394049,-2.346149,5.528978,6.765831,6.324425,13.803874,
15.007047,4.034973,12.383765,14.823395))
x <- c(0.75078002, 0.70959645 ,0.07482854,0.60755927 ,0.55037327 ,0.55037327,
0.35458257 ,0.21994714,0.66369585,0.12381099, 0.12381099)
mX <- as.matrix(cbind(constant = 1, x = x, x2 = x^2))
iN <- nrow(mX)
iK <- ncol(mX)
mXStacked <- (diag(iN)%x%mX)[-seq(from = 1,
to = iN*iN, by = iN+1), ]  # Stacked design matrix
vYStacked <- vec(vY%*%t(rep(1, iN)))[-seq(from = 1,
to = iN*iN, by = iN+1), ]   # Stacked outcomes
vBetaMinus <- solve(t(mXStacked)%*% mXStacked,
t(mXStacked)%*%vYStacked)           # estimated coefficients
mBetaMinus <- matrix(vBetaMinus, nrow = iK, ncol = iN)
vResid <- vY - diag(mX%*%mBetaMinus)                  # required residuals

matplot(vResid, type = "l", xlab = "Obs. index", ylab = "Residuals")           # plot the estimated residuals

This produces the following picture.

-
Thank you so much it was great. Well done –  nina Dec 2 '12 at 22:33
Thank you so much it was great. Well done.but this command (vYStacked) does not work in my r, please can you tell me what is the problem? Thanks –  nina Dec 2 '12 at 22:51
@nina You will need to install and load the Matrix and the matrixcalc libraries using install.packages("matrixcalc") and library(matrixcalc) (similarly for Matrix) before you run this code. –  T C Dec 3 '12 at 2:44
Theank you @Peter. Now it is working. Thank you once again.@Nina –  nina Dec 3 '12 at 11:34
May I asked why you offered to delete all this reply with your suggested edit, @nina? –  chl Dec 3 '12 at 12:07


text:
## Field equations

Consider an action $S$ depending on fields $\phi_{i}$, where the index $i$ labels both the field type, the component and the spacetime point. Add a term quadratically proportional to the field equations $S_{i}\equiv \delta S/\delta \phi _{i}$ and define the modified action

where $F_{ij}$ is symmetric and can contain derivatives acting to its left and to its right. Summation over repeated indices (including the integrationover spacetime points) is understood. Then there exists a field redefinition

with $\Delta _{ij}$ symmetric, such that, perturbatively in $F$ and to all orders in powers of $F$,

### Search this site

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### Book

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Renormalization

PDF

Last update: May 9th 2015, 230 pages

Contents: Preface | 1. Functional integral | 2. Renormalization | 3. Renormalization group | 4. Gauge symmetry | 5. Canonical formalism | 6. Quantum electrodynamics | 7. Non-Abelian gauge field theories | Notation and useful formulas | References

Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)


text:
# How to set working directory for Visual Studio 2017 RC CMake Project

I use Visual Studio 2017 RC to open a CMake project and then I find the working directory is always the output directory.

Is there any way to set the working directory to somewhere other than the directory of output file?

(Because there is no .sln file, I cannot set the working directory in the old way)

Update I am not calling programs from CMake scripts. I am running the target program in Visual Studio. And I want to change the working directory for the target program.

• For which purpose you want to change the working directory? If you run programs within add_custom_target() call, you may specify WORKING_DIRECTORY option for it. Jan 26, 2017 at 7:50
• @Tsyvarev I want to change the working directory of the output program so that some resource(such as images) can be shared between different configurations (Debug/Release).
– Null
Jan 26, 2017 at 8:06
• I want to change the working directory of the output program - Please, provide the code how you call this program from CMake script. (Do that in the question post itself, not in the comment). BTW, build directory (CMAKE_BINARY_DIR) is the same for all configurations. There are several artefacts (like libraries and executables) which are created in configuration-dependent directory). Jan 26, 2017 at 8:16
• @Tsyvarev You maybe misunderstand me. I am not calling the program from CMake script. I am running the target program in Visual Studio. I think it runs the CMake script and target program separately. And I want to change the working directory for the target program.
– Null
Jan 26, 2017 at 8:39
• Well, this explains a lot. I am running the target program in Visual Studio., And I want to change the working directory for the target program. - Please, add this into the question post itself, so your question will be clear without reading the comments. Jan 26, 2017 at 8:51

## 2 Answers

As of writing (2017-03-23), it is not possible to set working directory via CMakeLists.txt. Here are some workarounds:

# Using launch.vs.json

According to this bug report, you can add the setting inside your Debug and Launch Settings (right click the relevant CMakeLists.txt). This opens the launch.vs.json file, where you can add the working directory using the currentDir variable. Here's an example:

{
"version": "0.2.1",
"defaults": {},
"configurations": [
{
"type": "default",
"project": "CMakeLists.txt",
"projectTarget": "path\\to\\target",
"name": "My Awesome Project",
"currentDir": "${workspaceRoot}/src" } ] }  If you want you can go ahead and check that file in; it probably sits in .vs/launch.vs.json. • See the Visual C++ Team blog post. It doesn't mention currentDir though. • The syntax appears to be very similar to that used by Visual Studio Code, although the keywords are all different - VSCode uses cwd instead of currentDir, for example. # Using CMake >= 3.8.0 with VS_DEBUGGER_WORKING_DIRECTORY VS_DEBUGGER_WORKING_DIRECTORY is a new CMake target property in version 3.8.0. Set it like this: set_target_properties( MyProject PROPERTIES VS_DEBUGGER_WORKING_DIRECTORY "${CMAKE_SOURCE_DIR}/bin")

You need to use the old method of standalone CMake, generate .sln/.vcxproj files, open solution with Visual Studio, because the version of CMake integrated with Visual Studio 2017 is 3.6. Which leads to...

# Wait until Visual Studio ships with CMake >= 3.8.0

It's unknown when this will happen; the team are currently looking at updating to CMake 3.7 so it'll be a while longer. However when this happens chances are it will support the VS_DEBUGGER_WORKING_DIRECTORY property.

• Editing launch.vs.jsonworked for me. (Visual Studio 2017 Community) Nov 7, 2017 at 16:01
• Visual Studio 2017 15.6.1 now have cmake >= 3.8 support, and it still VS_DEBUGGER_WORKING_DIRECTORY unaware. launch.vs.json remains the only option! Mar 13, 2018 at 15:33
• For those, who are using VS to build over cmake for a remote system (e.g. Ubuntu 18.04), the VS_DEBUGGER_WORKING_DIRECTORY solution does not work, although using a cmake version >= 3.8.0. You have to use the launch.vs.json approach and set the "cwd" field instead of "currentDir". Also pay attention to use the correct macros for replacements of your local directories. E.g. the remote workspace root can be found with ${debugInfo.remoteWorkspaceRoot}. This was tested with VS Community 2017 , version 15.9.16. Dec 17, 2019 at 9:22 • Documentation for cmake json is here: learn.microsoft.com/en-us/cpp/build/… – c z May 10, 2022 at 14:55 Using currentDir, for example: { "version": "0.2.1", "defaults": {}, "configurations": [ { "type": "default", "project": "CMakeLists.txt", "name": "testd.exe (Debug\\testd.exe)", "currentDir": "${workspaceRoot}\\app_home",
"args": [
"\${workspaceRoot}\\app_home"
]
}
]
}

The reason why VS_DEBUGGER_WORKING_DIRECTORY not working is:
When we use VisualStudio IDE to manager a project, it just a text editor. For example a cmake project, the IDE just running cmake command by params in CMakeSettings.json

Then if we choose ninja, it will not generate the .sln and .vcproj files, just using build.ninja to drive build process.
If we choose Visual Studio 2019, it will generate a .sln file and some .vcproj file, but these file just a middle step of building. The current VS-IDE window will not load these file, just use command line to utilize the vcproj/sln file to build.
The VS_DEBUGGER_WORKING_DIRECTORY would saved into these middle-step .vcproj files, that invisible of current IDE windows. (Remember: The current IDE windows just a text editor of CMakeLists.txt)

In other words, it doesn't matter between using VS-IDE with cmake and makefile.

Note: We can see the build process in Output window.

Note: Whether we choose Ninja or VisualStudio2019, the backend build tools are same, MSVC.

But how can we use VS-IDE property? Just open the middle-step .sln and Visual Studio will automatically sync these two windows.


text:
# Unity 2d sprite repeated as background

I'm a web developer with over 12 years of experience and I'm moving my first steps in game development in the latest days. Specifically I'm playing with Unity and trying to understand how it works and how can I realize a 2d platform game. Currently I created a character that can be controlled with the keyboard (it moves to right, left and can jump), so far it seems more easy than I was expecting and despite I never used C# before I'm already quite comfortable. My first big concerning is about sprites and how can I create combined sprites or use an image as a repeated background. For example, let's imagine that I have a png of a brick and that I want to use it to create a wall, that can be of a variable width and height. How can I achieve that? With html/css I would simply create a class like this:

.wall {
background: url(brick.png);
}

and by applying that class to any html element it will render a repeated background by adapting it to its container no matter how large or tall is it. In unity/C# what should I do?

So far I tried to create a new material and applied it to a cube object but the result is that the image gets stretched and sucks. I saw some example that creates N sprites programmatically by adding them one after another, but I wonder about the performance implications of this technique... for example if I have to repeat the brick 100 times I have to create 100 objects, it seems unfeasible to me! What I want to achieve is the most flexible, simple and performant way to create "shapes" with repeated background.

So, I've recently done something along these lines and I'll put this here for future use.

This is the object I use for this effect:

Here's the script that modifies the object:

using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using UnityEngine.UI;

public class SlidingSpriteBackground : MonoBehaviour
{
public Sprite[] backgrounds;
public RawImage backgroundRenderer;
public float repeat = 3;
public float slidingSpeedX = .2f, slidingSpeedY = -.2f;
float moveByX, moveByY;
Resolution res;
Sprite useThis;
float horizontalTiles, verticalTiles;
int vTiles, hTiles;
// Use this for initialization
void Start()
{
res = Screen.currentResolution;
//this script uses a random background, you can set any kind of texture here
System.Random rnd = new System.Random(System.DateTime.Now.Minute);
useThis = backgrounds[rnd.Next(0, backgrounds.Length)];
//this part calculates the screen's size vs texture's size,
//so that you don't have to think about it
horizontalTiles = (float)Screen.width / (float)(useThis.texture.width);
verticalTiles = (float)Screen.height / (float)(useThis.texture.height);
//adds in the repeat amount you want in there
verticalTiles = verticalTiles * repeat;
horizontalTiles = horizontalTiles * repeat;
backgroundRenderer.texture = useThis.texture;
Rect uvRect = new Rect(0, 0, horizontalTiles, verticalTiles);
backgroundRenderer.uvRect = uvRect;

}

// Update is called once per frame
void Update()
{
//moves the sprite over time. if you want this to move with the player,
//you'll need to get the player location and move it according to that.
//(it should be relatively easy, but it'll take time to implement).
moveByX = moveByX + slidingSpeedX * Time.unscaledDeltaTime;
moveByY = moveByY + slidingSpeedY * Time.unscaledDeltaTime;
backgroundRenderer.uvRect = new Rect(moveByX, moveByY, horizontalTiles, verticalTiles);
//check if the screen size changed and recalculate
if (res.height != Screen.currentResolution.height
|| res.width != Screen.currentResolution.width)
{
horizontalTiles = (float)Screen.width / (float)(useThis.texture.width);
verticalTiles = (float)Screen.height / (float)(useThis.texture.height);
verticalTiles = verticalTiles * repeat;
backgroundRenderer.texture = useThis.texture;
horizontalTiles = horizontalTiles * repeat;
}
}
}

And here's what it looks like in effect (unfortunately I can't upload anything bigger because it goes over the 2MB limit):

As far as I understand your problem, you can try the following.

1. Firstly, depending on the screen resolution, you have to scale the background object so that it occupies the entire space. This can be done using the something like the following code.

newWidth = Screen.width / textureSize; newHeight = Screen.height / textureSize; transform.localScale = new Vector3(newWidth * textureSize, newHeight * textureSize, 1);

The variable textureSize is the size of your sprite.

1. Secondly, while applying the texture to the background object, you can add the tiling values so that the sprite is repeated instead of being stretched. This can be done using something like this.

GetComponent().material.mainTextureScale = new Vector3(newWidth, newHeight, 1);

I hope this helps you.

• mmm I think you get it wrong, I don't want a background for my scene, but instead I want to be able to create elements (like platforms you can jump on) with a repeated background... forgive me if I've been not clear, perhaps I'm using terms improperly since game development is not my field :P – daveoncode Jun 8 '16 at 9:30
• I am guessing that you don't have any problem with the creation of the new objects. Its just the repeated sprite part that is an issue. Right? In that case you can try the same approach as I mentioned in my answer to apply the sprite but instead of using the variables Screen. width and Screen.height, you can use the dimensions of your objects to find the tiling values newWidth, newHeight. – greenPadawan Jun 9 '16 at 7:16
• Yep, it's right – daveoncode Jun 9 '16 at 7:18
• Please have a look at the updated comment. – greenPadawan Jun 9 '16 at 11:08
• There are a couple of problems with this answer: 1. Unity doesn't support arbitrary texture scale & offset parameters on SpriteRenderers (it doesn't play nicely with the texture atlasing it's doing under the hood to save batches), but you can switch to quads with MeshRenderers to fix this. 2. Setting renderer.material will copy the material, so you'll end up creating unique materials for every object with this script, making them difficult to batch together and possibly leaking materials when these objects are destroyed (Unity doesn't clean up unused materials as readily as other garbage) – DMGregory Aug 12 '16 at 11:38


text:
# Base class for finite field elements¶

AUTHORS:

• David Roe (2010-01-14): factored out of sage.structure.element

• Sebastian Oehms (2018-07-19): added conjugate() (see trac ticket #26761)

class sage.rings.finite_rings.element_base.Cache_base
fetch_int(number)

Given an integer less than $$p^n$$ with base $$2$$ representation $$a_0 + a_1 \cdot 2 + \cdots + a_k 2^k$$, this returns $$a_0 + a_1 x + \cdots + a_k x^k$$, where $$x$$ is the generator of this finite field.

EXAMPLES:

sage: k.<a> = GF(2^48)
sage: k._cache.fetch_int(2^33 + 2 + 1)
a^33 + a + 1
class sage.rings.finite_rings.element_base.FinitePolyExtElement

Elements represented as polynomials modulo a given ideal.

Return the additive order of this finite field element.

EXAMPLES:

sage: k.<a> = FiniteField(2^12, 'a')
sage: b = a^3 + a + 1
2
1
charpoly(var='x', algorithm='pari')

Return the characteristic polynomial of self as a polynomial with given variable.

INPUT:

• var – string (default: ‘x’)

• algorithm – string (default: ‘pari’)

• ‘pari’ – use pari’s charpoly

• ‘matrix’ – return the charpoly computed from the matrix of left multiplication by self

The result is not cached.

EXAMPLES:

sage: from sage.rings.finite_rings.element_base import FinitePolyExtElement
sage: k.<a> = FiniteField(19^2)
sage: parent(a)
Finite Field in a of size 19^2
sage: b=a**20
sage: p=FinitePolyExtElement.charpoly(b,"x", algorithm="pari")
sage: q=FinitePolyExtElement.charpoly(b,"x", algorithm="matrix")
sage: q == p
True
sage: p
x^2 + 15*x + 4
sage: factor(p)
(x + 17)^2
sage: b.minpoly('x')
x + 17
conjugate()

This methods returns the result of the Frobenius morphism in the case where the field is a quadratic extension, say $$GF(q^2)$$, where $$q=p^k$$ is a prime power and $$p$$ the characteristic of the field.

OUTPUT:

Instance of this class representing the image under the Frobenius morphisms.

EXAMPLES:

sage: F.<a> = GF(16)
sage: b = a.conjugate(); b
a + 1
sage: a == b.conjugate()
True

sage: F.<a> = GF(27)
sage: a.conjugate()
Traceback (most recent call last):
...
TypeError: cardinality of the field must be a square number
frobenius(k=1)

Return the $$(p^k)^{th}$$ power of self, where $$p$$ is the characteristic of the field.

INPUT:

• k – integer (default: 1, must fit in C int type)

Note that if $$k$$ is negative, then this computes the appropriate root.

EXAMPLES:

sage: F.<a> = GF(29^2)
sage: z = a^2 + 5*a + 1
sage: z.pth_power()
19*a + 20
sage: z.pth_power(10)
10*a + 28
sage: z.pth_power(-10) == z
True
sage: F.<b> = GF(2^12)
sage: y = b^3 + b + 1
sage: y == (y.pth_power(-3))^(2^3)
True
sage: y.pth_power(2)
b^7 + b^6 + b^5 + b^4 + b^3 + b
is_square()

Returns True if and only if this element is a perfect square.

EXAMPLES:

sage: k.<a> = FiniteField(9, impl='givaro', modulus='primitive')
sage: a.is_square()
False
sage: (a**2).is_square()
True
sage: k.<a> = FiniteField(4, impl='ntl', modulus='primitive')
sage: (a**2).is_square()
True
sage: k.<a> = FiniteField(17^5, impl='pari_ffelt', modulus='primitive')
sage: a.is_square()
False
sage: (a**2).is_square()
True
sage: k(0).is_square()
True
matrix(reverse=False)

Return the matrix of left multiplication by the element on the power basis $$1, x, x^2, \ldots, x^{d-1}$$ for the field extension. Thus the emph{columns} of this matrix give the images of each of the $$x^i$$.

INPUT:

• reverse – if True, act on vectors in reversed order

EXAMPLES:

sage: k.<a> = GF(2^4)
sage: b = k.random_element()
sage: vector(a*b) == a.matrix() * vector(b)
True
sage: (a*b)._vector_(reverse=True) == a.matrix(reverse=True) * b._vector_(reverse=True)
True
minimal_polynomial(var='x')

Returns the minimal polynomial of this element (over the corresponding prime subfield).

EXAMPLES:

sage: k.<a> = FiniteField(3^4)
sage: parent(a)
Finite Field in a of size 3^4
sage: b=a**20;p=charpoly(b,"y");p
y^4 + 2*y^2 + 1
sage: factor(p)
(y^2 + 1)^2
sage: b.minimal_polynomial('y')
y^2 + 1
minpoly(var='x', algorithm='pari')

Returns the minimal polynomial of this element (over the corresponding prime subfield).

INPUT:

• var - string (default: ‘x’)

• algorithm - string (default: ‘pari’)

• ‘pari’ – use pari’s minpoly

• ‘matrix’ – return the minpoly computed from the matrix of left multiplication by self

EXAMPLES:

sage: from sage.rings.finite_rings.element_base import FinitePolyExtElement
sage: k.<a> = FiniteField(19^2)
sage: parent(a)
Finite Field in a of size 19^2
sage: b=a**20
sage: p=FinitePolyExtElement.minpoly(b,"x", algorithm="pari")
sage: q=FinitePolyExtElement.minpoly(b,"x", algorithm="matrix")
sage: q == p
True
sage: p
x + 17
multiplicative_order()

Return the multiplicative order of this field element.

EXAMPLES:

sage: S.<a> = GF(5^3); S
Finite Field in a of size 5^3
sage: a.multiplicative_order()
124
sage: (a^8).multiplicative_order()
31
sage: S(0).multiplicative_order()
Traceback (most recent call last):
...
ArithmeticError: Multiplicative order of 0 not defined.
norm()

Return the norm of self down to the prime subfield.

This is the product of the Galois conjugates of self.

EXAMPLES:

sage: S.<b> = GF(5^2); S
Finite Field in b of size 5^2
sage: b.norm()
2
sage: b.charpoly('t')
t^2 + 4*t + 2

Next we consider a cubic extension:

sage: S.<a> = GF(5^3); S
Finite Field in a of size 5^3
sage: a.norm()
2
sage: a.charpoly('t')
t^3 + 3*t + 3
sage: a * a^5 * (a^25)
2
nth_root(n, extend=False, all=False, algorithm=None, cunningham=False)

Returns an $$n$$th root of self.

INPUT:

• n – integer $$\geq 1$$

• extend – bool (default: False); if True, return an $$n$$th root in an extension ring, if necessary. Otherwise, raise a ValueError if the root is not in the base ring. Warning: this option is not implemented!

• all – bool (default: False); if True, return all $$n$$th roots of self, instead of just one.

• algorithm – string (default: None); ‘Johnston’ is the only currently supported option. For IntegerMod elements, the problem is reduced to the prime modulus case using CRT and $$p$$-adic logs, and then this algorithm used.

OUTPUT:

If self has an $$n$$th root, returns one (if all is False) or a list of all of them (if all is True). Otherwise, raises a ValueError (if extend is False) or a NotImplementedError (if extend is True).

Warning

The extend option is not implemented (yet).

EXAMPLES:

sage: K = GF(31)
sage: a = K(22)
sage: K(22).nth_root(7)
13
sage: K(25).nth_root(5)
5
sage: K(23).nth_root(3)
29

sage: K.<a> = GF(625)
sage: (3*a^2+a+1).nth_root(13)**13
3*a^2 + a + 1

sage: k.<a> = GF(29^2)
sage: b = a^2 + 5*a + 1
sage: b.nth_root(11)
3*a + 20
sage: b.nth_root(5)
Traceback (most recent call last):
...
ValueError: no nth root
sage: b.nth_root(5, all = True)
[]
sage: b.nth_root(3, all = True)
[14*a + 18, 10*a + 13, 5*a + 27]

sage: k.<a> = GF(29^5)
sage: b = a^2 + 5*a + 1
sage: b.nth_root(5)
19*a^4 + 2*a^3 + 2*a^2 + 16*a + 3
sage: b.nth_root(7)
Traceback (most recent call last):
...
ValueError: no nth root
sage: b.nth_root(4, all=True)
[]

ALGORITHM:

The default is currently an algorithm described in [Joh1999].

AUTHOR:

• David Roe (2010-02-13)

pth_power(k=1)

Return the $$(p^k)^{th}$$ power of self, where $$p$$ is the characteristic of the field.

INPUT:

• k – integer (default: 1, must fit in C int type)

Note that if $$k$$ is negative, then this computes the appropriate root.

EXAMPLES:

sage: F.<a> = GF(29^2)
sage: z = a^2 + 5*a + 1
sage: z.pth_power()
19*a + 20
sage: z.pth_power(10)
10*a + 28
sage: z.pth_power(-10) == z
True
sage: F.<b> = GF(2^12)
sage: y = b^3 + b + 1
sage: y == (y.pth_power(-3))^(2^3)
True
sage: y.pth_power(2)
b^7 + b^6 + b^5 + b^4 + b^3 + b
pth_root(k=1)

Return the $$(p^k)^{th}$$ root of self, where $$p$$ is the characteristic of the field.

INPUT:

• k – integer (default: 1, must fit in C int type)

Note that if $$k$$ is negative, then this computes the appropriate power.

EXAMPLES:

sage: F.<b> = GF(2^12)
sage: y = b^3 + b + 1
sage: y == (y.pth_root(3))^(2^3)
True
sage: y.pth_root(2)
b^11 + b^10 + b^9 + b^7 + b^5 + b^4 + b^2 + b
sqrt(extend=False, all=False)

See square_root().

EXAMPLES:

sage: k.<a> = GF(3^17)
sage: (a^3 - a - 1).sqrt()
a^16 + 2*a^15 + a^13 + 2*a^12 + a^10 + 2*a^9 + 2*a^8 + a^7 + a^6 + 2*a^5 + a^4 + 2*a^2 + 2*a + 2
square_root(extend=False, all=False)

The square root function.

INPUT:

• extend – bool (default: True); if True, return a square root in an extension ring, if necessary. Otherwise, raise a ValueError if the root is not in the base ring.

Warning

This option is not implemented!

• all – bool (default: False); if True, return all square roots of self, instead of just one.

Warning

The 'extend' option is not implemented (yet).

EXAMPLES:

sage: F = FiniteField(7^2, 'a')
sage: F(2).square_root()
4
sage: F(3).square_root()
2*a + 6
sage: F(3).square_root()**2
3
sage: F(4).square_root()
2
sage: K = FiniteField(7^3, 'alpha', impl='pari_ffelt')
sage: K(3).square_root()
Traceback (most recent call last):
...
ValueError: must be a perfect square.
trace()

Return the trace of this element, which is the sum of the Galois conjugates.

EXAMPLES:

sage: S.<a> = GF(5^3); S
Finite Field in a of size 5^3
sage: a.trace()
0
sage: a.charpoly('t')
t^3 + 3*t + 3
sage: a + a^5 + a^25
0
sage: z = a^2 + a + 1
sage: z.trace()
2
sage: z.charpoly('t')
t^3 + 3*t^2 + 2*t + 2
sage: z + z^5 + z^25
2
class sage.rings.finite_rings.element_base.FiniteRingElement
sage.rings.finite_rings.element_base.is_FiniteFieldElement(x)

Returns if x is a finite field element.

EXAMPLES:

sage: from sage.rings.finite_rings.element_base import is_FiniteFieldElement
sage: is_FiniteFieldElement(1)
False
sage: is_FiniteFieldElement(IntegerRing())
False
sage: is_FiniteFieldElement(GF(5)(2))
True


text:
# How to derive Van't Hoff equation for Henry's constant

While studying about Henry's Law, I encountered this equation,I didn't know how to derive it so I searched about it and got nothing, I tried to substitute $H$ (Henry's const.) by $\gamma\cdot f_i$ where $\gamma$ is activity coefficient at infinite dilution and $f_i$ is fugacity of pure species, but still had no idea what to do to reach a formula that I'm familiar with; so I welcome any idea about how to derive, or how to reverse engineering the formula.

• $\mathrm{d}\left(\frac1T\right)$ is $-\frac{1}{T^2}\cdot \mathrm dT$ and the $\frac{\Delta H}{RT^2}$ reminds me of some kind of $\Delta G$ equation:

$$\frac{\mathrm d\ln H}{\mathrm d(1/T)}= \frac{-\Delta_\textrm{sol}H }{R}\;.$$

Assuming Henry's coefficient $\mathcal{H}_i$ is defined by the following relation:

$$\mathcal{H}_i = \gamma_i^\inf \cdot p_i^\mathrm{sat}$$

Where $\gamma_i^\inf$ is the activity coefficient for an infinite diluted solution and $p_i^\mathrm{sat}$ is the vapor pressure of pure component $i$.

One can try to extrapolate Henry's coefficient at another temperature by assessing the following ratio (this is a common approach in Chemistry, not always valid):

$$\frac{\mathcal{H}_i(T_1)}{\mathcal{H}_i(T_0)} \approx \frac{\gamma_i^\inf(T_1) \cdot p_i^\mathrm{sat}(T_1)}{\gamma_i^\inf(T_0) \cdot p_i^\mathrm{sat}(T_0)}$$

The RHS maybe rearranged in order to have the well know form of ratio of mixed Equilibrium Constants $K_i$ considering that bulk concentration are close and ratio of activities also simplifies (over a small range of temperature).

$$\frac{\mathcal{H}_i(T_1)}{\mathcal{H}_i(T_0)} \approx \frac{\frac{\gamma_i(T_1)\cdot p_i(T_1)}{\eta_i(T_1)\cdot x_i(T_1)}}{\frac{\gamma_i(T_0)\cdot p_i(T_0)}{\eta_i(T_0)\cdot x_i(T_0)}} =\frac{K_i(T_0)}{K_i(T_0)}$$

That is, we are stating that ratio of Henri constants approximates ratio of equilibrium constant because we assume that only ratio of pressure is significant and other ratios tend to unity. This is, off course, not always acceptable, but in some restrained conditions it might hold.

Where the concerned reaction is the converse of gas solubilisation:

$$\mathrm{X}_{i,(\mathrm{aq})} \rightleftharpoons \mathrm{X}_{i,(\mathrm{g})}\quad \Delta_\mathrm{R}H = -\Delta_\mathrm{sol}H$$

And its mixed Equilibrium Constant:

$$K_i = \frac{\gamma_i\cdot p_i}{\eta_i \cdot x_i}$$

Then one may apply Van't Hoff relation using Enthalpy $\Delta_\mathrm{sol}H$ of the concerned reaction, from its integrated form, it comes:

$$\frac{\mathcal{H}_i(T_1)}{\mathcal{H}_i(T_0)} \approx \exp\left[\frac{\Delta_\mathrm{sol}H}{R}\left(\frac{1}{T_1}-\frac{1}{T_0}\right)\right]$$

This formulae is generally a good approximation around 20°C over a small range of temperature. Do not forget that $\Delta_\mathrm{sol}H$ is not a constant but rather a function of temperature.

If you wish to get your definition, you just have to differentiate the last relation with respect to temperature:

$$\frac{\mathrm{d}\ln(\mathcal{H}_i)}{\mathrm{d}T} \approx \frac{\Delta_\mathrm{R}H}{RT^2} = -\frac{\Delta_\mathrm{sol}H}{RT^2}$$

Or equivalently: $$\frac{\mathrm{d}\ln(\mathcal{H}_i)}{\mathrm{d}\left(\frac{1}{T}\right)} \approx -\frac{\Delta_\mathrm{R}H}{R} = \frac{\Delta_\mathrm{sol}H}{R}$$

• Can you please explain how you changed the right side of second equation? – Mo Samani May 24 '16 at 16:15
• assuming that ratio of $x's$ and ratio of activity coefficients are 1 right? so what's the formula used for $K$ here ? – Mo Samani May 24 '16 at 16:28
• How the equation for $Ki$ has obtained ? I know $K$ is the ratio of $fi$ to $fi$ (standard condition)، I understand the numerator,But Can't understand the denominator. – Mo Samani May 25 '16 at 10:17
• This is the expression of a mixed (polyphasic) equilibrium constant. $x_i$ stands for the bulk dissolved gas concentration at equilibrium and $\eta_i$ is its activity coefficient. It is just the ratio of product/reactant as you always write them for aqueous solutions. – jlandercy May 25 '16 at 11:35
• If you feel uncomfortable with this mixed constant, try convert it into $K_c$ or $K_p$. You will get some $RT$ terms that simply because of the ration of constants. – jlandercy May 25 '16 at 11:44


text:
## anonymous one year ago Calculate the integral of 8 - x from 0 to ten using the rule: As the limit N->∞ RvN

1. Astrophysics

What is RvN?

2. anonymous

I... I don't know. I'll just ask my teacher. It's like R then subscript N.

3. anonymous

Then behind it is lim N->∞

4. myininaya

I think maybe it is right endpoint rule?

5. anonymous

i think it means as the base of the rectangles goes to zero, but i could be wrong

6. myininaya

the RvN thing?

7. anonymous

$\lim_{N\to \infty}R_N$ ?

8. anonymous

@DurableToaster is gone, we will never know


text:
×

# Try to solve this

Prove that always exist integer number a,b,c such as $0< \left | a+b\sqrt{2} +c\sqrt{3}\right |< \frac{1}{1000}$

Note by Ms Ht
9 months, 3 weeks ago

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Hint: Show that for positive even integer $$n$$, $$(\sqrt 3 + \sqrt 2)^n + (\sqrt3 - \sqrt2)^n$$ is always an integer. · 9 months, 3 weeks ago

What about $$n = 1$$? Staff · 9 months, 3 weeks ago

Ahahaha, you've found a loophole. Let me fix it. · 9 months, 3 weeks ago

Nope, not fixed yet. It's not true for odd integers.

Essentially what you are doing is my approach 1 but with setting $$a = 0$$ (which complicates it just slightly). Staff · 9 months, 3 weeks ago

Awhhh!! I should have known! Fixed again~

Hmm... I don't see how mine is slightly harder than Approach 1, let me put my thinking cap on. · 9 months, 3 weeks ago

The slightly harder part being why we have to use $$2n$$ instead.

$$( 1 + \sqrt{2} ) ^n + ( 1 - \sqrt{2} ) ^ n$$ is an integer for all $$n$$, because odd powers of 1 is still an integer. Applying your approach results in $$c = 0$$. Staff · 9 months, 3 weeks ago

HA! That's a nice interpretation. ThankYou · 9 months, 3 weeks ago

Approach 1: Simplify the problem by setting $$c = 0$$.

Approach 2: Use Quadratic Diophantine Equations - Pell's Equation. Staff · 9 months, 3 weeks ago