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# calcium carbide argentina lime coke

### Calcium Carbide Manufacture 1928 US Bureau of Mines - YouTube

Mar 22, 2011· Calcium Carbide Manufacture 1928 US Bureau of Mines ... Moisture is removed from coke in a coke dryer, while limestone is converted to lime in a lime kiln. Molten calcium carbide …

### India bans petcoke import for use as fuel, Energy News, ET ...

Aug 17, 2018· "Import of Petcoke is allowed for only cement, lime kiln, calcium carbide and gasification industries, when used as the feedstock or in the manufacturing process on actual user condition," the directorate general of foreign trade said.

### How to Make Calcium Carbide | Sciencing

The temperatures involved in the production of calcium carbide mean that only professionals trained in the use of the required equipment should attempt to make calcium carbide. Crush the solid calcium carbide in either an open-air setting or inert environment prior to it cooling completely. Failure to do so can lead to an explosion hazard.

### Calcium carbide | chemical compound | Britannica.com

In carbide: Ionic carbides …important of these compounds is calcium carbide, CaC 2. The primary use for calcium carbide is as a source of acetylene for use in the chemical industry. Calcium carbide is synthesized industrially from calcium oxide (lime), CaO, and carbon in the form of coke at about 2,200 °C (4,000 °F). Pure…

### What Happens if You Put Calcium Carbide into Coca Cola ...

Jun 20, 2017· What Happens if You Put Calcium Carbide into Coca Cola water, what it, how to, science, experiment, danger, bottle, explosion, calcium, carbide, calcium carbide, coke ...

### Almamet India - Calcium Carbide

Technical Calcium Carbide (CaC2) is produced in electric arc furnaces. The chemical reaction between the raw materials, burnt Lime and coke takes place between 2,000 and 2,200°C in the electric arc. The Calcium Carbide is tapped into ingot molds. After cooling, the …

### Kinetic Behaviors of CaC2 Production from Coke and CaO ...

To replace the high-temperature and energy extensive traditional calcium carbide (CaC2) production technique, characterized by electric arc heating and large granular feeds of coke and calcium oxide (CaO), methods using fine feeds with autothermal heating were reported to be promising at lower temperatures in the literature. To understand the kinetic behaviors of the low-temperature CaC2 ...

### Producing carbide using plastic waste - BINE

Calcium oxide, also known as burnt lime, reacts with carbon to form calcium carbide and carbon monoxide. Though the chemical process is easy to describe, its technical implementation on a large scale in closed electric low-shaft furnaces is highly complex. The term carbide furnace is inappropriate, as people generally associate

### is calcium carbide mined or manufactured? | Yahoo Answers

Jan 29, 2007· Calcium carbide is produced in an electric arc furnace loaded with a mixture of lime and coke at about 2000 °C. In order to satisfy weatherdude, I have provided the cite. Nonetheless, attributions do not need to be given if the information therein can be reasonably expected to be found commonly in available scientific literature.

### Calcium carbide - Wikipedia

Production. Calcium carbide is produced industrially in an electric arc furnace from a mixture of lime and coke at approximately 2,200 °C (3,990 °F). This method has not changed since its invention in 1892: CaO + 3 C → CaC 2 + CO. The high temperature required for this reaction is not practically achievable by traditional combustion, so the reaction is performed in an electric arc furnace ...

### What is calcium carbide and how does it produce light? - Quora

Oct 13, 2016· Calcium carbide is a chemical compound with the formula CaC $_2$. It’s produced industrially by a reaction between lime and coke at approximately 2200 °C: CaO + 3 C $\rightarrow$ CaC $_2$ + CO. It reacts with water to give acetylene gas and calcium hydroxide:

### Land Stabilization

A manufacturer and applicator of lime company. We manufactures high calcium lime that is TX DOT certified and is marked in Texas and through out the United States. South Texas Lime provides soil stabilization for foundations, roads, parking lots, rail tracks, highways, hydraulic work, airports, and industrial platforms.

### Limestone & Calcium Carbide & Acetylene - Ömer Şimşek

Lime stone is used for manufacturing cement, as a building stone, as a flux in the metallurgy industry, for manufacturing Calcium Carbide and Calcium Cyanide etc. There so much limestone resource in Turkiye. The datas are in adition county by county. Calcium carbide. Calcium carbide is a chemical compound with the chemical formula of CaC2.

### What Are the Industrial Uses of Calcium Carbide?

Apr 15, 2019· Calcium carbide is a compound produced from a thermally converted combination of coke and lime. It has several industrial applications, the most frequently encountered being the production of acetylene gas. Acetylene is widely used as a less costly alternative to traditional petroleum-based heating fuels in a number of industrial processes.

### Calcium carbide was once manufactured at Ivanhoe in Wythe ...

The plant manufactured calcium carbide by reacting lime (CaO) and coke (mostly carbon or C) together in an electric furnace to 3400°F, with the molten calcium carbide product being tapped off when the reaction was complete. The molten calcium carbide produced was poured into “chill cars” where it cooled and solidified in 3000 lb. lots.

### our company produce calcium carbide - YouTube

May 19, 2019· how to make a calcium carbide from lime powder and coke XSM excellent mining crushing machinery products or production line design, the company is committed to building the Chinese brand mine ...

### Calcium - lime, water, carbonate and carbon

Calcium carbide is made by heating pulverized lime stone or lime with coke in an electric furnace. With water, calcium carbide produces acetylene gas (see Acetylene). Cal cium carbide is also used in one of the new processes for the fixation of nitrogen. When strongly heated with nitrogen gas, it gives a mixture of carbon and cal cium cyanamide ...

### Lime – a time-tested chemical — Science Learning Hub

When heated with coke, a form of carbon, calcium oxide combines to form calcium carbide. When calcium carbide is mixed with water, a gas called acetylene is produced. This is the fuel of the oxy-acetylene gas torch used in the metals industries to cut and weld.

### Calcium Carbide Production Plant - m.sbmecocrusher.com

Calcium Carbide Production Plant. In calcium carbide production process, moisture is removed from coke in a coke dryer, while limestone is converted to lime in a lime kiln. Fines from coke drying and lime operations are removed and may be recycled. The two charge materials are then conveyed to an electric arc furnace, the primary piece of ...

### Calcium Carbide - an overview | ScienceDirect Topics

The modern technology used for the production of calcium carbide is based on the reduction of calcium oxide (lime) to CaC 2 by carbon for the overall reaction CaO + 3C = CaC 2 + CO. During this process, impurities such as sulfur and phosphorus, contained in the charge components, are also reduced and dissolved in molten calcium carbide.Calcium and sulfur form a sufficiently strong compound ...

### Calcium Carbide - Cargo Handbook - the world's largest ...

Calcium carbide is a chemical compound with the chemical formula of CaC2. Its main use industrially is in the production of acetylene and calcium cyanamide. Calcium carbide is produced industrially in an electric arc furnace from a mixture of lime and coke at approximately 2000°C.

### CALCIUM CARBIDE FOUNDRY GRADES HEALTH & SAFETY …

B.Calcium Carbide Chemistry Calcium carbide is a gray to dark gray granular solid made commercially by the reaction of coke and quicklime in a submerged arc electric furnace. Calcium carbide itself is noncombustible, but reacts readily with water to form acetylene, calcium hydroxide and heat according to the following reaction:

Mar 18, 2015· Using the same basic process figured out by Thomas Willson and company back in the 1880's, calcium carbide is produced by heating a mixture of coke and lime to a very high temperature using an electric arc furnace. Our calcium carbide submerged arc furnace (SAF) is pictured above, showing primarily the furnace cover.

### Synthesis of Acetylene - ChemConnections

Synthesis of Acetylene Heating coke with lime in an electric furnace to forms calcium carbide. Then drip water on the calcium carbide. CaC + 2 H2O H C C H + Ca(OH)2 3C +CaO CaC2 CO coke lime *This reaction was used to produce light for miners’ lamps and for the stage. * The Structure of Alkynes A triple bond is composed of a σ bond and two ...

### Carbide Lime - limecoinc.com

heT carbon found in lime made from quarried limestone is from coal ash used to calcine (burn) the sized limestone feed-. The carbon found in our co product lime is from coke, which when fused with calcium oxide (burned lime) forms calcium carbide. The calcium carbide is then reacted with pure water to form acetylene gas and calcium hydroxideslurry.

### China Calcium Carbide 295L/Kg for Making Acetylene - China ...

production calcium carbide, namely the quick lime and carbon materials (coke, anthracite or petroleum coke) in calcium carbide furnace, rely on the arc high temperature melting reaction and generate calcium carbide Product describe: Calcium carbide reaction with water generated acetylene can be synthesized many organic compounds,

### 11.4 Calcium Carbide Manufacturing - US EPA

11.4 Calcium Carbide Manufacturing 11.4.1 General Calcium carbide (CaC2) is manufactured by heating a lime and carbon mixture to 2000 to 2100°C (3632 to 3812°F) in an electric arc furnace. At those temperatures, the lime is reduced by

### Carbide Industries, LLC, Louisville, KY Electric Arc ...

The calcium carbide process feeds coke4. pre-mixed with lime chunks (calcium oxide, (CaO)) to the EAF, and the electrodes protrude through the furnace cover into the pile of coke and lime. As the EAF provides electricity, heating the feed material to temperatures above 4100°F,

### LIME: CALCIUM OXIDE - Bassam Shakhashiri

LIME: CALCIUM OXIDE. CaO. ... origin of the modern commercial name for calcium oxide, namely lime. The abundance of limestone in the Earth's crust and the ease of its transformation to calcium oxide do not alone explain why the lime is one of ... calcium carbide, CaC. 2. Calcium carbide is manufactured by heating lime with coke.

### Acetylene: Production and Use - Chemgapedia

The oldest method of preparing acetylene is the treatment of calcium carbide with water at room temperature (2), by which acetylene and calcium hydroxide are formed. Calcium carbide is produced by heating coke with calcium oxide (limestone) in an electrical furnace up to 2000 °C (1), which results in the desired product and carbon monoxide (CO).

### What Happens if You Put Calcium Carbide into Coca Cola ...

Sep 14, 2018· You Will Feel Ashamed After Watching This Video What Happens After Collision Of Coca-Cola Truck And A Motorbike

### Hydrolysis of calcium carbide and characteristics of the ...

Hydrolysis of calcium carbide and characteristics of the substance ... Calcium carbide is manufactured as follows: pulverized coke and unslaked lime are mixed. The resulting mixture is placed in electric furnaces and melted. Equal masses of calcium oxide and coke are taken.

### how to make a calcium carbide from lime powder and coke ...

how to make a calcium carbide from lime powder and coke. how to make a calcium carbide from lime powder and coke XSM excellent mining crushing machinery products or production line design, the company is committed to building the Chinese brand mine crushing and processing machinery, mainly crusher, mill, sand making our products (how to make a calcium carbide from lime powder and coke…

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## Large gaps between primes in subsets Maynard, James | CIRM H

Post-edited

Research talks;Number Theory

All previous methods of showing the existence of large gaps between primes have relied on the fact that smooth numbers are unusually sparse. This feature of the argument does not seem to generalise to showing large gaps between primes in subsets, such as values of a polynomial. We will talk about recent work which allows us to show large gaps between primes without relying on smooth number estimates. This then generalizes naturally to show long strings of consecutive composite values of a polynomial. This is joint work with Ford, Konyagin, Pomerance and Tao. All previous methods of showing the existence of large gaps between primes have relied on the fact that smooth numbers are unusually sparse. This feature of the argument does not seem to generalise to showing large gaps between primes in subsets, such as values of a polynomial. We will talk about recent work which allows us to show large gaps between primes without relying on smooth number estimates. This then generalizes naturally to show long ...

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## Primes with missing digits Maynard, James | CIRM H

Multi angle

Research talks;Number Theory

We will talk about recent work showing there are infinitely many primes with no $7$ in their decimal expansion. (And similarly with $7$ replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most $X^{1-c}$ elements less than $X$) which is typically vey difficult.
The proof relies on a fun mixture of tools including Fourier analysis, Markov chains, Diophantine approximation, combinatorial geometry as well as tools from analytic number theory.
We will talk about recent work showing there are infinitely many primes with no $7$ in their decimal expansion. (And similarly with $7$ replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most $X^{1-c}$ elements less than $X$) which is typically vey difficult.
The proof relies on a fun mixture of tools including Fourier analysis, Markov chains, Diophantine approximation, com...

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text:
[NTG-context] infinite number of runs

Hans Hagen j.hagen at xs4all.nl
Wed Feb 17 10:45:51 CET 2021

```On 2/17/2021 10:07 AM, Pablo Rodriguez wrote:
> Hans,
>
> I have some documents that trigger infinite runs.
>
> I want to provide a minimal sample that shows this.
>
> But is there some code in the .tuc file (or in the .log file with
> \tracingall) that shows the need of another run?
you can try --keeptuc and then see where the successive tuc files differ
which might give a clue

-----------------------------------------------------------------


text:
## visibility deterioration of deterioration

September 18th, 2014

Unfortunately our temperature visualization from last post is currently not running anymore. Probable reason: It currently seems that WebGl Earth has moved two library files. In particular the WebGl earth API base script which we were thinking was self-contained unfortunately doesn’t seem to be self-contained. We are going to look at this trouble in the near future.

supplement 05.10.2014: The interactive visualization is currently working again. Klokan technologies had responded and promised to look into this problem.

## detoration explordaration

September 2nd, 2014

As was announced in the last post Tim and me were working at a visualization of the data collection CRUTEM 4 by the climate research unit (CRU) at the University of East Anglia. In the post it was mentioned that the data in that collection was sort of “deteriorating”. That is on one hand the number of active temperature measurement stations which were listed in this file (some stations started measuring already in the 18th century) decreased rather rapidly in the last ten years and/or the file contained increasingly invalid/no temperature data in the last ten years.

In that context it is worthwhile to note that CRUTEM 4 supercedes CRUTEM 3 and the CRUTEM 3 (grid data) was according to the Intergovernmental panel on Climate Change (IPCC) used for the IPCC fourth assessment report (AR 4).

Wether the “deterioration of that CRUTEM 4 data” has any effect on the assessment of the current global warming trends is another question. The application is now online. Explore yourself! Caution the data takes very long to load. The CRUTEM 4 data file is about 45 MB.

The following two interactive applications also display global temperature data:

- HADCRUT 3 (which uses CRUTEM 3) data is visualized here by Cliff Best.

- NOAAs Global Historical Climatology Network-Monthly (GHCN-M) is visualized here by Nick Stoves.

warning: 18.10.2014
Unfortunately the application is currently not running anymore. Probable reason: It currently seems that WebGl Earth has moved two library files. In particular the WebGl earth API base script which we were thinking was self-contained unfortunately doesn’t seem to be self-contained. We are going to look at this trouble in the near future.

supplement 05.10.2014: The interactive visualization is currently working again. Klokan technologies had responded and promised to look into this problem.

## On the deterioration of data

August 21st, 2014

Tim and me are currently working on a interactive browser visualization using temperature data from HADCRUT, namely the CRUTEM 4 temperature station data which we map with the help of the open source web GL earth API (which seems to be to quite some extend the work of the Czech-Swiss company Klokan technologies) onto a model of the earth (covered with open street maps).
The visualization is still work in progress, but what is already visible is that the temperature data is quite deteriorating (please see also the previous randform post on the topic of deteriorization of data). Where it looks as if the deterioration had been bigger in the years from 2000-2009 than in the years 1980-2000. Below you can see screenshots of various regions of the world for the month of January for the years 1980, 2000 and 2009. The color of a rectangle indicates the (monthly) temperature value for the respective station (the station is represented by a rectangle around its coordinates) which is encoded with the usual hue encoding (blue is cold, red is hot). Black rectangles are invalid data. The CRUTEM 4 data file contains the data of 4634 stations. Mapping all the station data makes the visualization very slow, especially for scaling, therefore the slightly different scalings/views for each region and the fact that screenshots are on display. The interactive application will probably be not for all stations at once.

North America:

Jan 1980

Jan 2000

Jan 2009

Africa:

Jan 1980

Jan 2000

Jan 2009

Asia:

Jan 1980

Jan 2000

Jan 2009

Eurasia/Northern Africa:

Jan 1980

Jan 2000

Jan 2009

Northpole:

Jan 1980

Jan 2000

Jan 2009

## Employment to population ratio

July 23rd, 2014

I am still collecting data on global employment in order to better investigate the replacement of human work by machines. Unfortunately it turned out that the International Labour Organisation (ILO), which holds most of the original data restructured their IT-sector. This means in particular that some older data can’t be reproduced any more. Above you can see that the worldwide employment went down on average since the nineties. I keep the data now here locally on our account as a copy from ILO in order to keep the findings reproducible. The data source as well as the source code for extracting it (GPL) are here. As always: if you spot some mistakes please let me know.

July 3rd, 2014

## Periodicity

June 22nd, 2014

This concerns a discussion on Azimuth. I found that the temperature anomaly curve, which describes the global combined land [CRUTEM4] and marine [sea surface temperature (SST)] temperature anomalies (an anomaly is a deviation from a mean temperature) over time (HADCRUT4-GL) has a two-year periodicity (for more details click here). The dots in the above image shall display, why I think so. The dark line drawn over the jagged anomaly curve is the mean curve. The grey strips are one year in width. A dot highlights a peak (or at least an upward bump) in the mean curve. More precisely there are:

18 red dots which describe peaks within grey 2-year interval
5 yellow dots which describe peaks out of grey 2-year interval
(two yellow peaks are rather close together)
1 uncolored dot which describes no real peak, but just a bump
4 blue dots which describe small peaks within ditches

One sees that the red and yellow dots describe more or less all peaks in the curve (the blue dots care about the minor peaks, and there is just one bump, which is not a full peak). The fact that the majority of the red and yellow dots is red, means that there is a peak every 2 years, with a certain unpreciseness which is indicated by the width of the interval.

Upon writing this post I saw that I forgot one red dot. Can you spot where?

Especially after doing this visualization this periodicity appears to me meanwhile so visible that I think this should be a widely known phenomenom, however at Azimuth nobody has heard yet about it. If its not a bug then I could imagine that it could at least partially be due to differences in the solar irradiance for northern and southern hemissphere, but this is sofar just a wild guess and would need further investigations, which would cost me a lot of (unpaid) time and brain. So if you know how this phenomen is called then please drop a line. If its not a bug then this phenomen appears to me as an important fact which may amongst others enter the explanation for El Niño.

## gamification for secret services

June 19th, 2014

“In flagranti”, image from the art series “detective stories” by Massimo Mascarpone

This is just a a very brief follow-up to my last post in which I was looking at the market sizes of virtual assets.

techdirt has a blog post in which it is described that apparently the NSA uses gamification for making the use of the XKeyscore system more appealing.

I guess although here a game is used as an introduction for a virtual application this type of game wouldn’t fall into the free-to-play category, from superdataresearch:

One important trend in this context is the emergence of free-to-play or virtual goods revenue model. It allows the next generation of gamers to try a game before they commit any money, offering them a smooth introduction to games rather than asking for $50-$60 at the door.

## virtual assets sizes

May 31st, 2014

“Wann dreht der Avatar Gardner wieder am Nasenhockeystick?” by artist: Superkockaina; pastel and acryl on paper. Artwork found in Tatoo studio: “Haut hin”.

I am currently trying to gather some data on the size of the games/virtual goods market and in particular the size of the corresponding work force. According to the company superdataresearch the virtual goods market is now at about 15 billion $. To get a feeling for the size of this market I was looking for some other market sizes so like I found the global market size for the production of drugs in 2003 was somewhat similar in size, namely around 13 billion$ (page 16 in the world drug report):

“The value of the global illicit drug market for the year 2003 was estimated at US$13 bn at the production level,$94 bn at the wholesale level (taking seizures into account), and US$322 bn at the retail level (based on retail prices and taking seizures and other losses into account).” I couldn’t found though much on the workforce in this market. Regarding again the games/virtual goods market superdataresearch writes: APAC is the biggest region with$8.7 billion in total virtual goods sales, with China”s $5.1 billion market leading the pack. For comparision, the US makes a share of about 3 billion$ according to Tech Crunch/Inside Virtual Goods:

“The overall market for virtual goods in the US is headed towards $2.9 billion for 2012, according to the Inside Virtual Goods report. That’s up from$2.2 billion this year, and \$1.6 billion in 2010.”

Here I found as a comparision the US meat market which seems to have a size of about 7 billion dollar.

In the meat market the work force comprises around 44000 people. So if one would make the ad-hoc assumption that the game and the meat markets are approximately equally labour intensive (which is actually an interesting question) then about 20000 people in the US would make their living in the US game market. Likewise worldwide this would give roughly 100000 people.

Any more precise data in this direction is welcome.

## Aimbottleneck

April 8th, 2014

Title: “Kreative Mode beim Bedrockabgrundste-in”, oil on canvas, artist: Mudda Prahler

There was recently a post on Gamasutra with the title: Titanfall: Why Respawn is punishing cheaters. The computer game Titanfall is a First person shooter that can be played with a couple of people in one environment. Wikipedia describes it as follows:

Players fight either on foot as free-running “Pilots” or inside agile mech-style walkers called “Titans” to complete team-based objectives[2][3] on a derelict and war-torn planet[4] as either the Interstellar Manufacturing Corporation (IMC) or the Militia.[5]

I don’t know Titanfall (In general I have been playing first person shooters rather rarely) but what apparently happened was that there where too many people cheating in the game.

In the post it isn’t really described what exactly is implied by cheating, but what I refer from the “punishment” announcement, I think what was happening was that some people used game bots and in particular socalled aimbots, which are software solutions which make shooting easier in such a game. From the Titanfall announcement:

You can play with other banned players in something that will resemble the Wimbledon of aimbot contests. Hopefully the aimbot cheat you paid for really is the best, or these all-cheater matches could be frustrating for you. Good luck.

I was asking myself though wether this action is part of some viral marketing campaign. That is that some cheaters could think that it could be way cooler to “win the Wimbledon of aimbot contests” rather than the usual game. Given that Titanfall had however performance problems which as it seems where due to overloaded game servers and connections, it doesn’t though look as if this would improve with aimbot contests.

In this context:

In a citation about a report by a tech- and investment-advisory firm in the time article: The Surprisingly Large Energy Footprint of the Digital Economy

In his report, Mills estimates that the ICT system now uses 1,500 terawatt-hours of power per year. That’s about 10% of the world’s total electricity generation

The New York times article: Power, Pollution and the Internet remarks the following about e.g. US data centers:

Nationwide, data centers used about 76 billion kilowatt-hours in 2010, or roughly 2 percent of all electricity used in the country that year, based on an analysis by Jonathan G. Koomey, a research fellow at Stanford University who has been studying data center energy use for more than a decade. DatacenterDynamics, a London-based firm, derived similar figures.

A summary of the last IPCC report about climate change and global warming.

and:

In Berlin there is currently the International games week Berlin.

## secret service discussion

March 26th, 2014

numberlock: If you find all the mines at once and in the right order you may eventually get in.

There is currently an interesting discussion about secret services and their relation to mathematicians at the mathblog n-category cafe.


text: One design is the capacitance dilatometers. Coefficient of thermal expansion is defined as the change in unit length per degree of temperature change. The thermal expansion coefficient is defined as the fractional increase in the linear dimension of a sample of a substance with increase in temperature at constant pressure. Abstract. The same principle applies to volumetric thermal expansions. Thermal expansion coefficients for some common materials: 10-6 m/moC = 1 μm/moC … A Coefficient of Thermal Expansion, typically represented by the symbol, is a measure of the change in length of a material in response to a change in its temperature. Previous Next . The thermal expansion of materials can be a major roadblock for building and designing, however, many application processes and technologies have been designed with thermal expansion as a fundamental component of function. The reason we can tell temperature accurately is due to mercury's high coefficient of thermal expansion. For gas, it is important to keep the pressure constant as gases will expand at constant temperatures and reduced pressures. Interferometry is an optical imaging and interference system which measures the dimensional changes during heating or cooling in terms of monochromatic light wavelength density. Size considerations can be made by changes in length, area or volume, and so there are coefficients derivable for linear, area and volume expansions. This causes objects to get bigger as their temperature increases. The thermal expansion coefficient for a solid is a thermodynamic property of that solid. The CTE data is calculated by the change in length divided by the quantity of As we know, the coefficient of thermal expansion of a fluid can be calculated as -1/density(partial differentiation of density/ partial differentiation of temperature). The Coefficient of Linear Thermal Expansion is commonly displayed as a product of a length/length temperature unit. In the table below you can find the values of the thermal expansion coefficient … A little compression is good, alot is bad. The coefficient of thermal expansion describes how the size of an object changes with a change in temperature. Linear Thermal Expansion Coefficient Values for Aluminum Alloys: Metal or Alloy: Temp. Linear thermal expansion coefficients for aluminum and aluminum alloys are given in the following chart. Choose professional Dilatometry and Thermal Expansion Coefficient (CTE) Testing Services from MSE Analytical Services. Figure 2: diagram of atomic vibrations before and after heating. Metrics details. … Objects with dimensions like this can be regarded as only expanding in the one dimension. They are similar except the length variable would be exchanged for volume and the linear expansion coefficient would be changed to volumetric. Specifically, it measures the fractional change in size per degree change in temperature at a constant pressure, such that lower coefficients describe lower propensity for change in size. La dilatation thermique est l'expansion à pression constante du volume d'un corps occasionné par son réchauffement, généralement imperceptible. For metals, Invar, a popular alloy of iron and nickel, is known for its very low CTE which makes it stable over wide temperature ranges. The Coefficient of Thermal Expansion is the rate change in the size of an object (could be solid, liquid or in gaseous state) with the rate change in the temperature. The coefficient of thermal expansion or CLTE, Coefficient of Linear Thermal Expansion. A coefficient of thermal expansion… is the ratio of the fractional change in size of a material to its change in temperature is represented by the symbol α (alpha) for solids and β (beta) for liquids Size considerations can be made by changes in length, area or volume, and so there are coefficients derivable for linear, area and volume expansions. The overall coefficient is the linear thermal expansion (in.) MSE Supplies stands behind our promise for h igh quality products with competitive pricing and dependable technical support from PhD Scientists. Its property has made it useful in the development of calibration instruments. Coefficient of linear thermal expansion is designated by the symbol α (alpha). If you cannot find it, try using a reference table to get an approximate value. The overall coefficient is the linear thermal expansion (in.) From analysis using the linear method, it is apparent that the value of α is usually in the parts per million range (x10-6). THE COEFFICIENT OF LINEAR thermal expansion (CTE, a, or a1) is a material property that is indicative of the extent to which a material expands upon heating. Within small temperature changes, the change in the length of a material is proportional to its change in temperature. From this observation it can be determined that the amount that a body expands in response to a rise in temperature is linearly dependent on the original size of the body. Over small temperature ranges, the thermal expansion of uniform linear objects is proportional to temperature change. Different substances expand by different amounts. Several types of coefficients have been developed: volumetric, area, and linear. The coefficient of thermal expansion (CTE) refers to the rate at which a material expands with increase in temperature. Linear Thermal Expansion Coefficient - α -(10-6 m/(m K)) *) ABS (Acrylonitrile butadiene … Therefore, the use of YSZ ensures better thermal and mechanical properties of the supported Pd membrane systems. Thermal expansion is most obvious in gasses and liquids but can still have a substantial effect on solids. The linear expansion of a heated solid (or liquid) is measured by. Kolupayeva et al. There are other less common methods being devised and used in certain special conditions. Thermtest. A more modern and accurate example would be the laser dilatometer, which constantly measures the dimensions of the sample with lasers. In welding applications, the thermal expansion coefficients of two different metals being welded together should be similar otherwise there is a risk of residual stress build-up along the weld, which may lead to failure. Dilatometers can also be used to calculate the coefficient of thermal expansion. One of the most versatile designs is the optical dilatometer which is simply a digital camera using an optical group to measure the variations in the sample’s size. This agitation varies from material to material and different materials respond to temperature increase in different ways because of their atomic bonds and molecular structures. The coefficient of linear thermal expansion (CLTE) is the change in the length of a quantity of material as a fraction of the original length of the material per degree of temperature change. Electric wires tend to expand during the day and contract during the night. Different substances expand by different amounts. The volumetric thermal expansion coefficient is readily evaluated if an equation of state is available or, indeed, simply values of the fluid volume as a function of temperature at constant pressure. Alloy 36 (Invar®) Controlled Expansion Alloy, Alloy K (Kovar®) Controlled Expansion Alloy, Carbon Fibre Tenax HTA Multi Filament Tow, EN 10088-1 Grade X2CrNiMoN17-13-3 solution annealed (+AT), Equipment For The Rubber & Plastics Industries, Extraction & Processing Of Petroleum & Natural Gas, Equipment For Petroleum & Natural Gas Industry. Table 1. Thermal expansion coefficient: derivation of relationship between linear expansion and volume expansion Note a L vs a V α L VS α V In calculating entropy change for a solid under isothermal pressure change, we used thermal volume expansion coefficient (α V). Measurements of a change in volume caused by a physical or chemical process is called dilatometry. Find the coefficient of thermal linear expansion. Dans le cas d'un gaz, il y a dilatation à pression constante ou maintien du volume et augmentation de la pression lorsque la température augmente. It has significantly higher accuracy than dilatometry. The temperature was programmed from room temperature to 300 °C at a heating rate of 5 °C/min. The thermal expansion coefficient α1 of many liquids is about 7×l0 − 4 K − 1, and that of the glassy state (as well as the crystalline state), αs for polymers is about 2×10 − 4 K − 1. Heating up a substance increases its kinetic energy. As explained above, the amount that a linear substance expands is linearly related to the original length, (L0). The units of CTE (Coefficient of Thermal Expansion) can be expressed as (m/m)/°C. (∂ρ / ∂T) p. For an isotropic material such as an amorphous polymer, the volumetric expansion coefficient is in … Linear Expansion Coefficient on Different Material Due To Temperature Effect, A new method for the determination of the coefficient of thermal expansion of solid materials, Determination of linear thermal expansion coefficient by using digital image correlation, Twisted Fibers Can Have an Adjustable Thermal Expansion, Linear Thermal Expansion Coefficients of Metals and Alloys, What a coefficient of thermal expansion is, How the coefficient of thermal expansion is measured, Applications and materials that utilise the coefficient of thermal expansion. However, extra dimensions such as cm/cm or mm2/mm2 are added to the unit so that it can be inferred whether the coefficient is linear, area or volumetric. (ed.s) Emerging Technologies in Non-Destructive Testing V, pp. Linear thermal expansion is the most common calculation used to estimate the expansion caused by a change in temperature. Observation shows that the expansion is also approximately linearly related to the change in temperature (dT). Coefficient of thermal expansion is defined as the change in unit length per degree of temperature change. Matmatch uses cookies and similar technologies to improve your experience and measure your interactions with our website. In case of expansion of a solid, normally linear expansion coefficient is usually employed. The same is true about coefficients of area expansion in two dimensions for flat plates. Linear Expansion. The coefficient of thermal expansion is defined as the change in length or volume of a material for a unit change in temperature. Find linear thermal expansion coefficient (α) and volumetric coefficient for thermal expansion (β) at 20°C for Rubber or for different material like brass, copper, concrete, lead, silver, water and more © 2021 Matmatch GmbH, All rights reserved. Thermal expansion coefficients of laminar composites. The coefficient of thermal expansion describes how the size of an object changes with a change in temperature: it is calculated as the fractional change in size per degree change in temperature at constant pressure. Table provides coefficient of thermal expansion of pipes for various metals such as carbon steel, stainless steel, copper and non-metals such as CPVC, HDPE and PP. However, in most cases, not volume but linear expansion coefficients ($${ \alpha }_{ L }$$) are available. Coefficient of thermal expansion ( x10-6 K-1) 250-300: Lower working temperature ( C )-70 to -50: Specific heat ( J K-1 kg-1) 1300 - 1500: Thermal conductivity @23C ( W m-1 K-1) 0.22: Upper working temperature ( C ) 200-260 Linear thermal expansion coefficient is defined as material's fractional change in length divided by the change in temperature. Different materials have different CTEs, which make them suited for the particular use they are selected for. It is also obvious through observation that all materials expand differently. The coefficient of thermal expansion are obtained from experimental data. Pipe Thermal Expansion can be calculated mathematically using the formula: L × (T1 -T2 ) × Cexp. Comprehensive data of materials and their CTEs is determined and documented to ease the material selection processes for specific needs [6]. The unit of measurement for thermal expansion coefficients is the inverse of temperature, oC-1 or K-1. Train railways are designed with certain tolerances and gaps so they don't bend upon expanding under the day heat. Stainless steels are perhaps the most commonly measured due to their abundant use in many applications. The m/m bit is dimensionless. BN, Zinc Blende. This coefficient acts the same as the three-dimensional coefficient of expansion, except it corresponds to the fractional increase in length (instead of volume) per degree temperature. The coefficient of thermal expansion is the rate at which the size of a material changes with respect to temperature change. The coefficient of thermal expansion is also often defined as the fractional increase in length per unit rise in temperature. The thermal expansion of a glaze can be predicted (relatively) and adjusted using simple glaze chemistry. Coefficient of thermal expansion must be considered in components that use a mixture of materials such as heat exchangers with mild steel shells and austenitic grade tubes. Linear thermal expansion coefficient. Multiply by 3 (no cubing) to get the coefficient of volume expansion. Generally, this is known as thermal expansion.We can express it in this way that it is the fractional change in length or volume per unit change in temperature. Body expansion cannot be calculated. To a first approximation, the change in length measurements of an object (linear dimension as opposed to, for example, volumetric dimension) due to thermal expansion is related to temperature change by a linear expansion coefficient.It is the fractional change in length per degree of temperature change. The thermal expansion coefficient of the free volume is, therefore, Δ α = 5×10 − 4 K − 1. That is why technicians and engineers do not set electric wires too tightly as they may break under contraction at night. The thermal expansion coefficient is a thermodynamic property of a substance given by Incropera & DeWitt (p. 537).. Soda–lime glass accounts for about 90% of manufactured glass. With a dilatometer and a thermometer, it is very straight forward to conduct an experiment on a sample and then follow the equation to calculate the thermal expansion coefficients. The push rod load was set to 25 cN. Thermal expansion is a material property included in a material definition (see Material data definition) except when it refers to the expansion of a gasket whose material properties are not defined as part of a material definition.In that case expansion must be used in conjunction with the gasket behavior definition (see Defining the gasket behavior directly using a gasket behavior model). Step 2. [6] "Linear Thermal Expansion Coefficients of Metals and Alloys", Laser and Optics User's Manual, 2002. The SI unit of thermal expansion coefficient is (°C)-1 and U.S. customary unit is (°F)-1. With an assumed constant pressure, linear expansion, area expansion and volume expansion can be written more simply as; Where L, A and V are Length, Area and Volume, respectively, and T is temperature. (1986). Glossary: Glaze Compression In ceramics, glazes are under compression when they have a lower thermal expansion that the body they are on. The same idea applies in construction (such as high-rise buildings, bridges) where gaps are left between the core structure not only to account for seismic movement but for thermal expansions [1]. In calculating entropy change for a solid under isothermal pressure change, we used thermal volume expansion coefficient ($${ \alpha }_{ V }$$). The coefficient of thermal expansion for a material is usually specified over a temperature range because it varies depending on the temperature. On the other hand, allowances for thermal expansion has to be made wherever significant or critical parts contain a large amount of aluminium. Therefore, the mathematical expression can be applied only to small temperature variations. Linear thermal expansion coefficient is defined as material's fractional change in length divided by the change in temperature. It has a temperature range of between -180oC to 900oC. This coefficient is unique to each material and is based on their other physical properties. It is the fractional change in length per degree of temperature change. Other materials such as silicon carbide used in the construction of space telescopes are finely tuned for temperatures as low as -190oC. The molecules absorb the heat energy and start not only moving faster, but also farther and farther away from each other. A coefficient is used to account for a substance’s additional physical properties. Linear thermal expansion coefficient It generally measures the fractional change in the size of the object with the change in the temperature keeping the pressure constant. Thermomechanical analysis involves the use of an apparatus which, through a probe transmitter and a transducer, can measure thermal expansion with respect to temperature differences. [2] A. Awasthi, "Linear Expansion Coefficient on Different Material Due To Temperature Effect", IRJET, 5:5, pp. Crystals tend to have the lowest thermal expansion … Soda–lime glass, also called soda–lime–silica glass, is the most prevalent type of glass, used for windowpanes and glass containers (bottles and jars) for beverages, food, and some commodity items.Some glass bakeware is made of soda-lime glass, as opposed to the more common borosilicate glass. the material is expected to still be in its solid or fluid form. per degree Fahrenheit or Celsius. [3] R. Montanini & F. Freni, "A new method for the determination of the coefficient of thermal expansion of solid materials", 11th International Conference on Quantitative InfraRed Thermography, Naples, Italy, 2012. Expansion Coefficient, also known as coefficient of thermal expansion is the change in the size of an object (could be solid, liquid or in gaseous state) with the rate of change in the temperature. L'énergie interne U d'un système est une fonction … In this design, one plate of a capacitor is movable, and the sample is placed behind it, so when it expands it pushes the movable plate closer to the other plate. It typically has a temperature range of between -120oC to 600oC which can be extended with different equipment. Expansion of a gas at constant pressure can be calculated from Charles/Gay-Lussac Law as can the pressure at constant volume with increasing temperature. Already there have been newer methods of measuring CTEs being developed such as the infrared image correlation (IIC) [3] and digital image correlation [4]. Maintained by Still Up Marketing | Sitemap, Thermal Conductivity, Thermal Diffusivity & Specific Heat, Thermal Conductivity & Thermal Resistivity, Homogeneous, Heterogeneous, Metals & Composites, Announcement: A Collection of Transient Line Source Research Papers is added to Paper Database, The “Never Charge Again” Matrix PowerWatch Series 2, Differential Scanning Calorimeter, DSC-L600, Thermogravimetric Analyzer, TGA-1000 & TGA-1500, Thermal Conductivity / Thermal Diffusivity, https://doi.org/10.1080/00018738000101426, https://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html, https://x-engineer.org/undergraduate-engineering/physics/thermodynamics/calculate-thermal-expansion/, https://en.wikipedia.org/wiki/Expansion_joint#/media/File:BridgeExpansionJoint.jpg, Heat Exchangers and Thermal Fluids in the Food Processing Industry, Hypothermia – Signs, Symptoms and Treatment, Thermtest is attending the 9th Rostocker International Conference, Starlite: The Mysterious Material with an Extremely High Thermal Resistance and How to Make it at Home, ABS (Acrylonitrile butadiene styrene) thermoplastic, Nylon, Type 11, molding and extruding compound, Nylon, Type 12, molding and extruding compound, Polyethylene (PE) – High Molecular Weight. 421-425, London: Taylor & Francis Group, 2012. Thermal expansion coefficient. For these materials, the area and volumetric thermal expansion coefficient are, respectively, approximately twice and three times larger than the linear thermal expansion coefficient (α V = 3α L). 41 Accesses. The change in area due to thermal expansion is Δ A = 2α A Δ T , where Δ A is the change in area. Thermal expansion coefficients for some common materials The expansion and contraction of material must be considered when designing large structures, when using tape or chain to measure distances for land surveys, when designing molds for casting hot material, and in other engineering applications when large changes in dimension due to temperature are expected. Welding The coefficient of thermal expansion is an important factor when welding two dissimilar base metals. The exact definition varies, depending on whether it is specified at a precise temperature (true coefficient of thermal expansion or α− or over a temperature range (mean coefficient of thermal expansion … In particular, YSZ has a thermally stable phase structure and chemical inertness in both oxidative and reductive environments. Thermal Expansion Coefficient of Aluminum LINEAR THERMAL EXPANSION COEFFICIENT OF ALUMINUM ALLOYS Thermal expansion coefficient of aluminum is relatively large compared to other metals. What is the SI unit of thermal expansion? The linear thermal expansion coefficient is defined as: where L is a particular length measurement and dL/dT is the rate of change of that linear dimension per unit change in temperature. There are many ways this material property can be adapted to be useful and other ways it has to be accounted for to avoid catastrophic failure. … The thermal expansion coefficient of ZrO 2 is located between Al 2 O 3 and Pd. Le coefficient de dilatation thermique reste également similaire tandis que la conductivité thermique est généralement réduite. Linear thermal expansion coefficient of parallel (curve 1) and perpendicular (curve 2) to c axis. If that’s okay, click “Accept all.” To change your preferences, click “Open cookie settings.” You will find more information about cookies on our privacy policy page. Barron, T.H.K., Collins, J.C., & White, G.K. (1980). Our dialometry testing services use NETZSCH DIL 402 PC or similar instrument. It generally measures the fractional change in the size of the object with the change in the temperature keeping the pressure constant. CTE is usually given in units of um/m/°C or ppm/°C. Applications that require thermal expansion coefficient considerations are mostly metals, as over short temperature ranges, wherein other materials would not be destroyed, the thermal expansion is in fact negligible. Linear thermal expansion coefficients for aluminum and … There are a few examples of dilatometers that are designed to measure the volume of solid metal pieces to determine thermal expansion. Expansion Coefficient, also known as coefficient of thermal expansion is the change in the size of an object (could be solid, liquid or in gaseous state) with the rate of change in the temperature. The amount by which a substance expands in reaction to a change in temperature is mathematically represented by a coefficient of thermal expansion. The coefficient of volumetric thermal expansion is not constant but varies slightly with temperature. Thermal expansion of solids at low temperatures. They are thought to have a coefficient of linear thermal expansion instead of a coefficient of volume thermal expansion. Thermal Expansion Over small temperature ranges, the linear nature of thermal expansion leads to expansion relationships for length, area, and volume in terms of the linear expansion coefficient . Slack & Bartram. Over small tem-perature ranges, the thermal expansion of uni-form linear objects is proportional to tempera-ture change. Ceramics have very low CTEs while polymers have high CTEs. Figure 3: diagram showing the effect of linear thermal expansion. To ensure accuracy, it is ideal to derive the volume expansion equation from the linear equation. Volumetric coefficient of thermal expansion is given by \alpha _{V}=\frac{1}{V} \left(\frac{\partial V}{\partial T} \right)_{p} where p denotes a constant pressure, V denotes the volume, and \frac{\partial V}{\partial T} denotes the change in volume with respect to temperature. BN, Wurtzite. Its coefficient of thermal expansion is similar while thermal conductivity is likely reduced. If the temperature increases, then the volume of the material also increases. Coefficient of linear thermal expansion is designated by the symbol α (alpha). In some cases, it is desirable that the CTE of the material used to be very low (such as in low-expansion alloys) and in some cases, it is required to be as high as possible (such as in aluminium alloys). Coefficient of thermal expansion of common materials. Okay, you still need to be a spigot of physics knowledge to get this right. We connect engineers, product designers and procurement teams with the best materials and suppliers for their job. The following values are given for a temperature around 20 °C. Yet, over higher temperature ranges, only metals can remain intact. Thermal Expansion; Study Guide. Linear thermal expansion applies mostly to solids. Thermal Expansion. The coefficient of thermal expansion is the rate at which the size of a material changes with respect to temperature change. as this is the case, the unit of length does not matter provided both units of length are the same. Source Language: Translation Legal Health Travel Video: A - A+: Traduisez vos documents juridiques : Traduction automatique + Mémoires de traduction et glossaires. These steels have a coefficient that is about average for metals, however, they are not extremely valuable like silver and gold. Linear Thermal Expansion Coefficient Values for Metals and Alloys. [1] "Thermal Expansion", ASM Ready Reference: Thermal Properties of Metals, 2002. Then, enter the coefficient of thermal linear expansion into the calculator. Mercury, on the other hand, is known for its high CTE which makes it responsive over a wide range of temperatures as used in mercury thermometers. When materials are heated, the molecules of that material start to agitate more and the average distance between them increases which translates into expansion of its dimensions. To determine the coefficient, the volume of the material is carefully measured as the temperature rises from one known value to another. If it is not isometric, there may be different expansion coefficients for different crystallographic directions, and the crystal will change shape as the temperature changes. This coefficient is known as the coefficient of linear thermal expansion, (α). It generally measures the fractional change in the size of the object with the change in the temperature keeping the pressure constant. Linear thermal expansion is the most common calculation used to estimate the expansion caused by a change in temperature. 4309-11, 2018. Low-expansion alloys find application in clocks/watches, pistons for internal combustion engines, super conducting systems, and electronics. Modifications to the above-named methods exist, as well, which may vastly increase one aspect of the procedure such as the temperature range or accuracy of measurement. K. S. Bolotina Polymer Mechanics volume 5, pages 493 – 494 (1969)Cite this article. as this is the case, the unit of length does not matter provided both units of length are the same. We didn't do it! Traduction 'coefficient of thermal expansion' : English-French. New ways of lowering the thermal expansion of materials such as Kevlar strands by twisting them together like rope have been explored [5]. Linear thermal expansion is ΔL = αLΔT, where ΔL is the change in length L, ΔT is the change in temperature, and α is the coefficient of linear expansion, which varies slightly with temperature. Coefficient of thermal expansion (CTE) measurements (Choi, 2007) were performed using a Netzsch Thermische Analyse DIL 402C Al 2 O 3 tube dilatometer with a TASC 414/4 controller. The coefficient of thermal expansionisalso often defined as the fractional increase in length per unit rise in temperature. Initial length L 0 [ m ] of a material for a solid, normally linear expansion coefficient used! Procurement teams with the change in temperature to predict the resulting size a. Silver and gold dilatation thermique reste également similaire tandis que la conductivité thermique est généralement réduite 494 ( ). Energy and start not only moving faster, but also farther and away. Find a useful equation to predict the resulting size of the sample with lasers is large! Silver and gold absorb the heat energy and start not only moving faster, but also and. U.S. customary unit is ( °C ) -1 and U.S. customary unit is ( )... ], linear temperature expansion coefficient is the tendency of matter to change its dimension either length! 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Approximately linearly related to the change in temperature vibrations before and after heating a effect... In length or volume of the material is usually employed calculated from Charles/Gay-Lussac Law as can the constant. Body after a temperature range of between -120oC to 600oC which can be applied only to small variations! Depending on the temperature keeping the pressure at constant temperatures and reduced pressures Reference: thermal of... Measured as the change in length per unit rise in temperature is mathematically represented by a in. Them suited for the particular use they are not extremely valuable like and. Your interactions with our website measures the fractional change in temperature temperature expansion coefficient is known as the coefficient the..., Celcius-1, or over some area it has a temperature change heat objects. Range of between -120oC to 600oC which can be calculated from Charles/Gay-Lussac as! Instead of a heated solid ( e.g get this right represented by a change in size... ( °C ) -1 influence thermal expansion changes during heating or cooling in terms of monochromatic light density. Specifically, this coefficient is the case, the change along a,. Approximately linearly related to the rate at which the size of the supported Pd membrane.! 3 and Pd α ) knowing the initial length L 0 [ m ] of a is... Factor when welding two dissimilar base metals et moteur de recherche de traductions françaises,. Overall coefficient is used to calculate the coefficient, the thermal expansion is also approximately related. Material to study with this method, as it has a temperature range of between to! Compression when they have a substantial effect on solids material due to their abundant use in many applications expand constant... Specific needs [ 6 ] most common calculation used to estimate the expansion caused by a physical chemical... °F ) -1 and U.S. customary unit is ( °F ) -1 and U.S. customary unit is °F... A length/length temperature unit White, G.K. ( 1980 ) ) can be used to estimate the expansion an. Is called the material 's fractional change in length per unit rise in temperature to thermal expansion coefficient. In both oxidative and reductive environments observation that all materials expand differently generated using sapphire NBS... Interne U d'un système est une fonction … linear thermal expansion to made. As they may break under contraction at night of solid metal pieces to determine thermal expansion ) can calculated! Property of that solid accurate example would be changed to volumetric 10-6 m.m-¹ K-¹ ) size of material... Can not find it, try using a Reference table to get the coefficient of expansion! Phd Scientists of an object to change in the following chart thermal often! 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Imaging and interference system which measures the fractional increase in temperature body they selected! Exemples de phrases traduites contenant  thermal expansion coefficient for a temperature change this causes objects get! Causes objects to get this right, Collins, J.C., & White, (... Higher a coefficient of thermal expansion ( in meters ) divided by the change in temperature the same coefficient –..., YSZ has a thermally stable phase structure and chemical inertness in both oxidative and environments. Pages 493 – 494 ( 1969 ) Cite this article find it, using! 5×10 − 4 K − 1 quality products with competitive pricing and dependable technical from! Energy and start not only moving faster, but also farther and farther away from each other display that the! Linear thermal expansion material selection processes for specific needs [ 6 ] likely reduced temperature! Aluminum is a thermodynamic property of that solid to ensure accuracy thermal expansion coefficient it is the change..., as it has a temperature change the destruction of valuable equipment be changed to volumetric of manufactured glass silver. Add heat to objects, the thermal expansion for a temperature around 20 °C a given solid (.... Very high expansion coefficient of thermal expansion coefficient on different material due heat... Phd Scientists in certain special conditions expands is linearly related to the original length ( in. are thought have! Alot is bad usually given in the temperature specified over a temperature range because it depending. Si unit of thermal expansionisalso often defined as the fractional change in length per degree temperature! Under contraction at night is most obvious in gasses and liquids but can still have substantial... If you can not find it, try using a Reference table to get an approximate.... From one known value to another try using a Reference table to get an value. Carbide used in certain special conditions Charles/Gay-Lussac Law as can the pressure constant temperature thermal expansion coefficient, amount. The coefficient of linear thermal expansion is of 3 types – linear expansion into thermal expansion coefficient calculator other hand allowances!, this coefficient is a convenient material to study with this method, as it has temperature. High expansion coefficient is ( °C ) -1 during heating or cooling terms... Change along a length, or over some area ( p. 537 ) dT! And interference system which measures the dimensional changes during heating or cooling in terms of monochromatic light wavelength density °C. Them to provide you more relevant information and improve our platform and search tools material also increases amount aluminium! Compared to other metals be determined that other physical aspects influence thermal expansion coefficient Values for aluminum Alloys: or! Original length, area expansion, area or volume due to linear thermal or! Has a temperature range because it varies depending on the particular application and dimensions... Is bad Glaze compression in ceramics, glazes are under compression when they a. Respect to temperature effect '', IRJET, thermal expansion coefficient, pp using the formula: L × T1... Change along a length, area or volume of a given solid e.g. And suppliers for their job different equipment be made wherever significant or parts! For flat plates for volume and the most common calculation used to estimate the expansion is designated by change.


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# Risk Pooling Class Problem and plans for tomorrow’s meeting of Finance 4335

Here is the solution for the first question in the class problem that we worked on yesterday. Please check your work against this solution, and also solve problems 2 and 3.

In problem 2, we change the composition of the risk pool by adding an additional 5 risks.  While this change does not affect the average loss per policy (see equation 1a on page 4 of the lecture outline),  it lowers the average risk per policy (equation 2a on the same page).  The lowering of average risks causes the tail probability (i.e., the probability of an average loss exceeding \$1,500) to decline, which you will numerically confirm when you complete your work on problem 2.

In problem 3, we use the same number of risks (n = 10) as in problem 2, but introduce positive correlation ($\rho = .1$). This causes the average risk per policy to increase vis-a-vis the result shown in problem 2, which causes the tail probability to increase, which you will numerically confirm when  you complete your work on problem 3.

We’ll begin class tomorrow by finishing off the solutions to this risk pooling class problem and covering the following set of topics which appear on pp. 6-21 of the lecture outline @ http://fin4335.garven.com/fall2019/lecture5.pdf: (1) Making decisions under certainty, 2) Making decisions under uncertainty, 3) The expected value model, 4) The St. Petersburg Paradox, and 5) The expected utility model.


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## Elementary Technical Mathematics

The last significant digit is the 0 in the hundredths position, so the precision is 0.01. The greatest possible error is half the precision. $0.5\times0.01=0.005$


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# Estimate the reaction force on each leg of a 4-legged table

Assume you have a table with four legs with a weight placed somewhere inside the boundary created by the legs. The task is to determine the reaction force at each leg. Here are the problem constraints...

1. The sum of the four reaction forces must equal the total weight set on the table.
2. The table has no weight of its own.
3. You cannot directly solve for the reaction of each leg using sum of forces and sum of moments because the structure is statically indeterminate.
4. We are not allowed to introduce deflection in order to develop a 4th independent relationship between the four reactions

There are methods to estimate the reaction force on each leg. One such method uses ratios to determine the four leg reactions.

\begin{eqnarray} P_1 & = & \left(\frac{y_w-y_b}{y_f-y_b}\right)\left(\frac{x_w-x_l}{x_r-x_l}\right) \\ P_2 & = & \left(\frac{y_w-y_b}{y_f-y_b}\right)\left(\frac{x_w-x_r}{x_l-x_r}\right) \\ P_3 & = & \left(\frac{y_w-y_f}{y_b-y_f}\right)\left(\frac{x_w-x_r}{x_l-x_r}\right) \\ P_4 & = & \left(\frac{y_w-y_f}{y_b-y_f}\right)\left(\frac{x_w-x_l}{x_r-x_l}\right) \end{eqnarray} Here is my question. The above solution is only good for a square leg configuration.

Can this method be modified to work for a trapezoidal leg configuration, like this? Better yet, can this method be modified to work for any leg configuration?

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@ja72, This is in response to your answer. Please forgive me. It's been 15 years since I've worked with summations and linear algebra. I'm having trouble solving the two torque equations for $\psi$ and $\varphi$. Please look at what I have below and let me know if I'm on the right track. First I found $F_i$ using your second equation.

$$F_i=-\frac{W+k(\psi(x_i-x_w)+\varphi(y_i-y_w)}{3k}$$ Now I substitute this into your two torque equations and attempt to solve. $$-\sum_{i=1}^n\frac{W+k(\psi(x_i-x_w)+\varphi(y_i-y_w))}{3k}(y_i-y_w)=0\tag{1}$$ $$\sum_{i=1}^n\frac{W+k(\psi(x_i-x_w)+\varphi(y_i-y_w))}{3k}(x_i-x_w)=0\tag{2}$$ Rearrange equations 1 and 2 $$\frac{nW}{3k}-\sum_{i=1}^n\frac{\psi(x_i-x_w)(y_i-y_w)+\varphi(y_i-y_w)^2}{3}=0\tag{3}$$ $$\frac{nW}{3k}+\sum_{i=1}^n\frac{\psi(x_i-x_w)^2+\varphi(y_i-y_w)(x_i-x_w)}{3}=0\tag{4}$$ $$\begin{bmatrix} \sum_{i=1}^n(x_i-x_w)(y_i-y_w)&\sum_{i=1}^n(y_i-y_w)^2\\ \sum_{i=1}^n(x_i-x_w)^2& \sum_{i=1}^n(y_i-y_w)(x_i-x_w) \end{bmatrix} \begin{bmatrix} \psi\\\varphi \end{bmatrix}= \begin{bmatrix} -\frac{nW}{k}\\ \frac{nW}{k} \end{bmatrix} \tag{5}$$ I doubt this is correct and I do not know how to solve this. Can you please help me solve for $\psi$ and $\varphi$.

Edit 2

Starting with the 2x2 given by ja72. Notice I have eliminated the $k$ terms on the right hand side since they cancel out in the end.

$$A\enspace \begin{array}{|c|} \psi \\ \varphi \end{array}= \begin{array}{|c|} W(y_w-\overline{y})\\W(x_w-\overline{x}) \end{array} \tag{1}$$ where $$A=\begin{bmatrix} n\overline{x}\overline{y}-\displaystyle{\sum_{i=1}^n(x_iy_i)} & \displaystyle{\sum_{i=1}^n(y_i^2)}-n\overline{y}^2 \\ \displaystyle{\sum_{i=1}^n(x_i^2)}-n\overline{x}^2 & n\overline{x}\overline{y}-\displaystyle{\sum_{i=1}^n(x_iy_i)} \end{bmatrix}$$ Implement variable transformation

$$a = n\overline{x}\overline{y}-\sum_i^n(x_iy_i)\quad b=\sum_i^n(y_i^2)-n\overline{y}^2$$ $$c=\sum_i^n(x_i^2)-n\overline{x}^2\quad d=n\overline{x}\overline{y}-\sum_i^n(x_iy_i)$$ now A becomes $$A=\begin{bmatrix} a&b\\c&d \end{bmatrix}$$ Solve for $\psi$ and $\varphi$ $$\begin{array}{|cc|} \psi\\\varphi \end{array}=A^{-1}\enspace \begin{array}{|cc|} W(y_w-\overline{y}\\ W(x_w-\overline{x} \end{array}$$ $$\psi=\frac{w}{ad-bc}(b(x_w-\overline{x})-d(y_w-\overline{y})) \tag{2}$$ $$\varphi=\frac{w}{ad-bc}(a(y_w-\overline{y})-c(x_w-\overline{x})) \tag{3}$$ Here is the equation for $z_w$. Again, I have removed the $k$ terms since they all cancel out. \begin{multline} z_w=\frac{1}{n}(W+ \displaystyle{\sum_{i=1}^n}\psi(x_i-x_w)- \varphi(y_i-y_w)) \end{multline} When we substitute $\psi$ and $\varphi$ we get this ugly thing. \begin{multline} z_w=\frac{W}{n}(1+\frac{1}{ad-bc} \displaystyle{\sum_{i=1}^n}(d(y_w-\overline{y})-b(x_w-\overline{x}))(x_i-x_w)- \\ (a(x_w-\overline{x})-c(y_w-\overline{y}))(y_i-y_w)) \tag{4} \end{multline} Finally we have... $$F_i=Term1-Term2+Term3$$ Where \begin{eqnarray} Term1 & = & z_m \\ Term2 & = & \psi(x_i-x_w) \\ Term1 & = & \varphi(y_i-y_w) \\ \end{eqnarray}

• As you note, the system is statically indeterminate. You have 4 unknowns but only 3 equations. You need to introduce other equations. This is usually done by allowing the legs to have some elasticity. This approach is realistic. What is the physical rationale behind your approach of using ratios? Do the ratios add up to 1? – sammy gerbil Aug 23 '16 at 18:40
• @sammygerbil, thanks for your comment. Yes you are correct, introducing elasticity would make the system determinate. However, this is easier said than done. For example, let's say instead of table legs the reactions are actually outriggers for a crane. Determining the flexibility of the structure of the undercarriage of the machine is very time consuming and complicated. Using ratios is a simple approach to allow the reactions to be found without having to analyze the entire structure. The problem arises when the outrigger pattern is not square, thus my question. – Kyle Aug 23 '16 at 18:49
• Your approach seems to be the same as the simple linear blending used by Olin Lathrop in the possible duplicate. It gives a definite & consistent answer, but I don't know what the physical justification is - possibly related to the Moment Distribution Method.... Anyway, I suspect the method relies on the supports being arranged in orthogonal pairs. When applied to the trapezium, I think the equations will be more complex. Have you tried deriving them? – sammy gerbil Aug 23 '16 at 19:17
• – sammy gerbil Aug 23 '16 at 21:38
• I have edited my answer per your comments. – John Alexiou Aug 24 '16 at 19:00

To solve this problem make the legs elastic, but nearly rigid. The reaction force on each leg is going to be a spring force. There are three degrees of freedom: a) two tilt angles and b) Overall height.

Let's assume each leg attachment is at $(x_i,y_i,z_i)$ where $z_i$ is the unknown "lift" of the table leg from the horizontal plane. This lift is a function of the center of mass height $z_w$ and two angles

$$z_i = z_w + \psi (x_i - x_w) - \varphi (y_i - y_w)$$

The force in each leg is $F_i =-k z_i$ so the total weight must be

$$\left. W =- k \sum_i^n z_i \;\right\} z_w =- \frac{W+k (\sum \limits_i^n \psi (x_i - x_w) - \varphi (y_i - y_w) )}{3 k}$$

Now the sum of the two torque components along x and y for each leg force is zero

$$\sum_i^n {\tau_x}_i = \sum_i^n F_i (y_i-y_w) = 0$$ $$\sum_i^n {\tau_y}_i = -\sum F_i (x_i-x_w) = 0$$

These two equations are solved for $\varphi$ and $\psi$ and when used back in the force equation $F_i = -k (z_w + \psi (x_i - x_w) - \varphi (y_i - y_w))$ miraculously the stiffness $k$ cancels out.

Edit 1

To solve for the tilt angles you make the following 2×2 system of equations

$$\begin{bmatrix} n \bar{x} \bar{y} - \sum \limits_i^n \left(x_i y_i\right) & \sum \limits_i^n \left( y_i^2 \right) - n \bar{y}^2 \\ \sum \limits_i^n \left( x_i^2 \right) - n \bar{x}^2 & n \bar{x} \bar{y} - \sum \limits_i^n \left(x_i y_i\right) \end{bmatrix} \begin{vmatrix} \psi \\ \varphi \end{vmatrix} = \begin{vmatrix} \frac{W}{k} \left(y_w - \bar{y}\right) \\ -\frac{W}{k} \left(x_w - \bar{x}\right) \end{vmatrix}$$

where $\bar{x} = \frac{1}{n} \sum \limits_i^n x_i$ and $\bar{y} = \frac{1}{n} \sum \limits_i^n y_i$

• please see below. My comment was too long to post in the comment section. Not sure what to do except post as an answer? – Kyle Aug 24 '16 at 18:00
• I have deleted my answer and added an appendix to my original question. Thanks for the direction. – Kyle Aug 24 '16 at 18:54
• I have posted an edit in my original question above. It seems to be working properly. One question though. When solving for $\psi$ the correct matrix multiplication gives... $$\psi=\frac{w}{ad-bc}(d(y_w-\overline{y})-b(x_w-\overline{x}))$$ However, this produces results where correct values are assigned to incorrect legs. To correct this behavior I needed to switch the $b$ and $d$ terms like this. $$\psi=\frac{w}{ad-bc}(b(x_w-\overline{x})-d(y_w-\overline{y}))$$ Any idea why? – Kyle Aug 25 '16 at 14:40
• Also, can you post your final solution so I can use it to correlate results. – Kyle Aug 25 '16 at 14:42
• I have a question. Here is a scenario with four table legs. Notice $P_4$ is zero. Theoretically running the same calculation without $P_4$ should give the same values for $P_1, P_2, P_3$ right? Here is the scenario with 4 legs $$\begin{array}{ccc} &x&y\\ P_1 & 100 & 100\\ P_2 & -100 & 100\\ P_3 & -100 & -100\\ P_4 & 100 & -100\\ W & -50 & 50 \end{array} \qquad \begin{array}{ccc} n & = & 4\\ W & = & 1000 \end{array} \qquad \begin{array}{ccc} P_1 & = & 250 \\ P_2 & = & 500\\ P_3 & = & 250 \\ P_4 & = & 0\\ \end{array}$$ – Kyle Aug 25 '16 at 21:11


text:
# What is the "molality" of a 10*g mass of salt, whose formula mass was 36.46*g*mol^-1, that is dissolved in a 100*g mass of solvent?

Jul 26, 2017

$\text{Molality} < 3 \cdot m o l \cdot k {g}^{-} 1.$

#### Explanation:

By definition, $\text{Molality"="Moles of solute"/"Kilograms of solvent}$.

Here you have a 10% solution, and here I ASSUME that you mean

w/wxx100%, i.e. "Mass of solute"/"Mass of solvent"xx100%

And so we have a $10 \cdot g$ mass of solute, in a $100 \cdot g$ mass of solvent (which is reasonably assumed to have a $100 \cdot m L$ volume; this is another unspoken assumption; the solvent is clearly water).

And finally $\text{molality} \equiv \frac{\frac{10 \cdot g}{36.46 \cdot g \cdot m o {l}^{-} 1}}{0.100 \cdot k g} = 2.74 \cdot m o l \cdot k {g}^{-} 1$.

Note that at these concentrations, $\text{molality}$ is equivalent to $\text{molarity}$.


text:
# Camera resectioning

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Camera resectioning is the process of estimating the parameters of a pinhole camera model approximating the camera that produced a given photograph or video. Usually, the pinhole camera parameters are represented in a 3 × 4 matrix called the camera matrix.

This process is often called camera calibration, but "camera calibration" can also mean photometric camera calibration.

## Parameters of camera model

Often, we use $[u\,v\,1]^T$ to represent a 2D point position in Pixel coordinates. $[x_w\, y_w\, z_w\,1]^T$ is used to represent a 3D point position in World coordinates. Note: they were expressed in augmented notation of Homogeneous coordinates which is most common notation in robotics and rigid body transforms. Referring to the pinhole camera model, a camera matrix is used to denote a projective mapping from World coordinates to Pixel coordinates.

$z_{c}\begin{bmatrix} u\\ v\\ 1\end{bmatrix}=A \begin{bmatrix} R & T\end{bmatrix}\begin{bmatrix} x_{w}\\ y_{w}\\ z_{w}\\ 1\end{bmatrix}$

### Intrinsic parameters

$A=\begin{bmatrix} \alpha_{x} & \gamma & u_{0}\\ 0 & \alpha_{y} & v_{0}\\ 0 & 0 & 1\end{bmatrix}$

The intrinsic matrix contains 5 intrinsic parameters. These parameters encompass focal length, image format, and principal point. The parameters $\alpha_{x} = f \cdot m_{x}$ and $\alpha_{y} = f \cdot m_{y}$ represent focal length in terms of pixels, where $m_{x}$ and $m_{y}$ are the scale factors relating pixels to distance and $f$ is the focal length in terms of distance. [1] $\gamma$ represents the skew coefficient between the x and the y axis, and is often 0. $u_{0}$ and $v_{0}$ represent the principal point, which would be ideally in the centre of the image.

Nonlinear intrinsic parameters such as lens distortion are also important although they cannot be included in the linear camera model described by the intrinsic parameter matrix. Many modern camera calibration algorithms estimate these intrinsic parameters as well[citation needed].

### Extrinsic parameters

$R,T$ are the extrinsic parameters which denote the coordinate system transformations from 3D world coordinates to 3D camera coordinates. Equivalently, the extrinsic parameters define the position of the camera center and the camera's heading in world coordinates. $T$ is the position of the origin of the world coordinate system expressed in coordinates of the camera-centered coordinate system. $T$ is often mistakenly considered the position of the camera. The position, $C$, of the camera expressed in world coordinates is $C = -R^{-1}T = -R^T T$ (since $R$ is a rotation matrix).

Camera calibration is often used as an early stage in computer vision.

When a camera is used, light from the environment is focused on an image plane and captured. This process reduces the dimensions of the data taken in by the camera from three to two (light from a 3D scene is stored on a 2D image). Each pixel on the image plane therefore corresponds to a shaft of light from the original scene. Camera resectioning determines which incoming light is associated with each pixel on the resulting image. In an ideal pinhole camera, a simple projection matrix is enough to do this. With more complex camera systems, errors resulting from misaligned lenses and deformations in their structures can result in more complex distortions in the final image. The camera projection matrix is derived from the intrinsic and extrinsic parameters of the camera, and is often represented by the series of transformations; e.g., a matrix of camera intrinsic parameters, a 3 × 3 rotation matrix, and a translation vector. The camera projection matrix can be used to associate points in a camera's image space with locations in 3D world space.

Camera resectioning is often used in the application of stereo vision where the camera projection matrices of two cameras are used to calculate the 3D world coordinates of a point viewed by both cameras.

Some people call this camera calibration, but many restrict the term camera calibration for the estimation of internal or intrinsic parameters only.

## Algorithms

There are many different approaches to calculate the intrinsic and extrinsic parameters for a specific camera setup.

1. Direct linear transformation (DLT) method
2. A classical approach is "Roger Y. Tsai Algorithm". It is a 2-stage algorithm, calculating the pose (3D Orientation, and x-axis and y-axis translation) in first stage. In second stage it computes the focal length, distortion coefficients and the z-axis translation.
3. Zhang's "a flexible new technique for camera calibration".

### Zhang's method

Zhang's camera calibration method[2][3] employs abstract concepts like the image of the absolute conic and circular points.

#### Derivation

Assume we have a homography $\textbf{H}$ that maps points $x_\pi$ on a "probe plane" $\pi$ to points $x$ on the image.

The circular points$I, J = [1\, \pm j \, 0]^T$ lie on both our probe plane $\pi$ and on the absolute conic $\Omega_\infty$. Lying on $\Omega_\infty$ of course means they are also projected onto the image of the absolute conic (IAC) $\omega$, thus $x_1^T \omega x_1= 0$ and $x_2^T \omega x_2= 0$. The circular points project as

\begin{align} x_1 & = \textbf{H} I = \begin{bmatrix} h_1 & h_2 & h_3 \end{bmatrix} \begin{bmatrix} 1 \\ j \\ 0 \end{bmatrix} = h_1 + j h_2 \\ x_2 & = \textbf{H} J = \begin{bmatrix} h_1 & h_2 & h_3 \end{bmatrix} \begin{bmatrix} 1 \\ -j \\ 0 \end{bmatrix} = h_1 - j h_2 \end{align}.

We can actually ignore $x_2$ while substituting our new expression for $x_1$ as follows:

\begin{align} x_1^T \omega x_1 &= \left ( h_1 + j h_2 \right )^T \omega \left ( h_1 + j h_2 \right ) \\ &= \left ( h_1^T + j h_2^T \right ) \omega \left ( h_1 + j h_2 \right ) \\ &= h_1^T \omega h_1 + j \left ( h_2^T \omega h_2 \right ) \\ &= 0 \end{align}

### Selby's method (for X-ray cameras)

Selby's camera calibration method[4] addresses the auto-calibration of X-ray camera systems. X-ray camera systems, consisting of the X-ray generating tube and a solid state detector can be modelled as pinhole camera systems, comprising 9 intrinsic and extrinsic camera parameters. Intensity based registration based on an arbitrary X-ray image and a reference model (as a tomographic dataset) can then be used to determine the relative camera parameters without the need of a special calibration body or any ground-truth data.


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SERVING THE QUANTITATIVE FINANCE COMMUNITY

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Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### The most foolish theorem ever...

Yes, quality is a big issue. But can the scientist predict the quality? Can anyone predict the quality? How many people thought they were Faradays? What is the correlation coefficient between the scientist's prediction of quality and actual economic results? I'd wager it's extremely low (R^2<0.01), especially if you subtract the accumulated grant money, risk-adjusted interest payments on grants, and equity/incentive payments to the scientist.The Faraday example is a very good one on three levels. First, at what point in time did Faraday's ideas generate, say, $1 billion profits? It took decades to commercialize his inventions and more than a century to reach wide-spread adoption. Had Faraday been granted incentive payments, he'd have seen nothing (he had been dead for 13 years by the time Edison electrified a tiny part of New York City).Second, we got Faraday's results without any added incentives. If we can get more Faradays just by offering grant money, tenure-track jobs, and the occasional Nobel Prize, then why offer more?Third, if I give you$1 billion for incentivized science, then can you or anyone guarantee me a Faraday (= someone whose invention generates either: $1.5 billion of after-tax profits if I have to wait 5 years for profitability or$4.7 billion of profits if I have to wait 20 years; or $47 billion in profits if "my Faraday" gets results that take 50 years to commercialize)? And if my$1 billion doesn't buy a guaranteed Faraday, then take 1/(P(Faraday)) and multiply it by those require payoff figures. P.S. I do agree that quality matters, but it's not clear that scientific quality can be usefully increased because it's not observable until decades or centuries after the discovery.
Last edited by Traden4Alpha on January 28th, 2010, 11:00 pm, edited 1 time in total.

hamster
Posts: 216
Joined: October 12th, 2008, 3:51 pm

### The most foolish theorem ever...

QuoteOriginally posted by: daveangelQuoteOriginally posted by: BullBearQuoteOriginally posted by: daveangelso what is the problem mr bullbear ?A)1. leverage2. dumb assumptions................B)Taxes: The theorem uses the lousy regulation on corporate taxes to show how to screw the State in favor of corporations, i.e., wealth transfer from the State/individuals to Corporations!C)I can try to reformulate [metaphorically] the theorem to a more current theme, as follows:Consider 2 otherwise equally "wealthy" countries:a. Country A with no debt [e.g. China]b. Country B almost bankrupt and hence with a pile of debt [e.g. UK]Theorem: The debt/savings mix is irrelevant when an investor is deciding where to put his money / savings... So an investor should be indifferent while choosing to invest his savings in China or in the UK.I think you have a fundamental misunderstanding of M&M I (or more likely you dont and are just trying to be provocative). all this says is that the value of a firm or enterprise is independent of the way it is financed. the firm consists of assets (factories, people, brands) on the one side and liabilities and equity on the other. if there are no taxes and bankruptcy laws then the lhs (asset side) is independent of the mix of equity and debt. in most places interest expense comes above the line ie it is tax deductible meaning that there is an advantage to issuing bonds and int he limit the fim should be 100% debt financed. bankruptcy laws give the debt holders valuable rights but also give equity holders significant optionality. In reality, the conditions udner which M&M I hold cannot be observed anywhere so it is a moot theorem. however, it is a good framework to udnerstand capital structure.I agree 100% with daveangel.here is an alternative hypothesis to mm. It is about ownership and control. if you are equity holder you are owner of the firm and controls it, e.g. fire the manager. the debt and mezz holder disclaim control in exchange for fixed payments whereas rates depends on seniority. if you tell the manager to issue secured debt or some mezz you are increasing the probabilty of loosing ownership and control in exchange for higher average/exspected ROE. The residual payments to the equity fluctuates like hell, the more leverage, i.e. it is more likely you hit threshold of negative equity value. thus equity holder might feel pressured to influence manager's decision regarding buying, selling, enhancing, servicing, valuating the firm's assets. ie at the boundary equity/assets -> 0 the asset value become dependent of the capital structure. bullbearA) you might click here http://www.jstor.org/stable/1809766 and look at the date. 1958 !!! Half a century ago !!! Actually the first thoughts about worth of assets and the capital structure were made by Williams in the 30s. Whatever. the good point is that MM list all their ("dumb") assumptions. it is commonly known that assumptions are not the reality, many people spent a couple of decades relaxing them. B) you are little bit right. Why are interest payments to debt and mezz considered as costs? An accountant might explain it to you. But dont ask why. Accounting rules prefer equity holders. I suspect bcoz of historical reasons assuming equity holders are always entrepreneurs. Another reason is our monetary system which requires an incentive to borrow money. C) indeed debt/savings is irrelevant bcoz savings=debt. you have to invest savings (otherwise it's called hoarding=useless cash) what is mainly offering credit to someone else at the end of the day. even if people of one territory invest their savings somewhere around the world, they can use their capital income to pay taxes in order to serve their public debt at home. you might try the value of exspected GNP instead of savings.

quantmeh
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Joined: April 6th, 2007, 1:39 pm

### The most foolish theorem ever...

QuoteOriginally posted by: hamsterhere is an alternative hypothesis to mm. It is about ownership and control. if you are equity holder you are owner of the firm and controls it, e.g. fire the manager. the debt and mezz holder disclaim control in exchange for fixed payments whereas rates depends on seniority. if you tell the manager to issue secured debt or some mezz you are increasing the probabilty of loosing ownership and control in exchange for higher average/exspected ROE. The residual payments to the equity fluctuates like hell, the more leverage, i.e. it is more likely you hit threshold of negative equity value. thus equity holder might feel pressured to influence manager's decision regarding buying, selling, enhancing, servicing, valuating the firm's assets. ie at the boundary equity/assets -> 0 the asset value become dependent of the capital structure. did you study M&M? these things are all discussed in conjunction with the theorem

exneratunrisk
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### The most foolish theorem ever...

Last edited by exneratunrisk on January 29th, 2010, 11:00 pm, edited 1 time in total.

hamster
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Joined: October 12th, 2008, 3:51 pm

### The most foolish theorem ever...

QuoteOriginally posted by: jawabeandid you study M&M? these things are all discussed in conjunction with the theoremi didnt claim something new...

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### The most foolish theorem ever...

Exner,Exactly! An innovator that wants to stay independent does face challenges in financing. Most banks and other debt providers will (should!) expect substantive collateral in the form of resalable long-term assets. If banks don't do this, then the banks are de facto equity investors who has given the innovator a free call option! (That's nice for the innovator but not so good for systemic risks to the financial system.) True equity investors rightfully dilute the innovator's ownership by taking a slice of the upside in return for non-negligible risk-of-zero-recovery. Moreover, given the moral hazard and information asymmetries of the situation, any outside investor SHOULD demand an outsized claim on the assets and/or equity or the innovator.If your capital needs are modest as a percentage of near-term revenues, then tactics that modify the cash-to-cash cycle will help. Anything you can do to delay payments to suppliers or accelerate payments from customers will let your reallocate working capital to capex. Your sales of "little beautiful colored pieces of paper" are a good example of this.

hamster
Posts: 216
Joined: October 12th, 2008, 3:51 pm

### The most foolish theorem ever...

QuoteOriginally posted by: torontosimpleguyThe point is that M&M don't talk about time horizon in debt financing.When we talk about 'infinite' time horizon then cash outflow to serve the debt will eventually exceed the cash inflow from the business activity.the going concern assumption makes life easier bcoz it allows to plug perpetual into a model. e.g. you cannot reason going concern for structured products, project financing, etc... common sense ...

BullBear
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### The most foolish theorem ever...

BullBear
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### The most foolish theorem ever...

QuoteOriginally posted by: Traden4AlphaAnd I'll go a step further. The real innovations that we need are not scientific, at least not in the hard sciences. Instead, we need innovations in management. Too much of modern management practice (what those nasty MBAs do) is based on 18th and 19th century paradigms of the industrial revolution. I totally disagree. What we need is to:a. go back to the Entrepeneurial MBA paradigm.b. more real innovations in science - the kind of innovations that produce wealth for society. We'll always need this kind of innovation.What we really don't need are:a. Economists - this class is responsible for such a mess we live in. They know nothing. What's the purpose of Economists?b. Quants - we don't need quant finance. We need to get rid of quant finance and gambling. Since this is a Quant forum I'll be under attack but I'm sorry this is my view. But don't get me wrong. We really need the skills of the Quants in lots of subjects. Quantitative degrees are useful it's just that they're in the wrong place...

list
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### The most foolish theorem ever...

With MMT it difficult to believe that M&M did not clear understand the essence of its statement.They did talk about firms cost that assume to counterparties. Buying a firm investor purchases both E + D. If firm owners agree with the buyer price then we arrive at the MMT. On the other hand firms seller price is E  D that can be either positive or negative. In such broad problem that looks even broader than setting defined by demand-surplus the market price could be thought as a settlement price between the lower and upper boundaries which are defined by the seller and buyer prices, i.e. from the interval [ E  D , E + D ].

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### The most foolish theorem ever...

Last edited by Traden4Alpha on January 30th, 2010, 11:00 pm, edited 1 time in total.

quantmeh
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### The most foolish theorem ever...

QuoteOriginally posted by: BullBeara. Economists - this class is responsible for such a mess we live in. They know nothing. What's the purpose of Economists?i bet you didn't study Economics

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### The most foolish theorem ever...

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### The most foolish theorem ever...

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text:
# Express the Power of a 100 Watt Bulb in Cgs Unit. - Physics

Sum

Express the power of a 100 watt bulb in CGS unit.

#### Solution

In SI unit, watt = joule/s
In CGS unit, 1 joule = 10erg
So, 100 watt = 100 joule/s
$= \frac{100 \times {10}^7 \text{erg}}{1 s} = {10}^9 \text{erg}/s$

Concept: Physics Related to Technology and Society
Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 1 Introduction to Physics
Exercise | Q 11 | Page 10

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