text:
# Testing the CRE Package

We encourage all developers to test the package in different conditions. Testing the package is the easiest way to get familiar with the package and its functionalities.

# Getting the code

To test the package, please install the package on your system (R (>= 3.5.0)). You can install the package by following one of these approaches:

• Directly from GitHub
• CRAN (not recommended)
• Source
• Forked Repository (recommended)

## Installing the package directly from Github

In this project, we follow A successful Git Branching Model. As a result, the develop branch is the most updated branch for developers. Use devtools::install_github to install the package. If you do not specify the ref, it will install the master (or main) branch.

library(devtools)
try(detach("package:CRE", unload = TRUE), silent = TRUE) # if already you have the package, detach and unload it, to have a new install.
install_github("NSAPH-Software/CRE", ref="develop")
library(CRE)

Try ?CRE. It should open the package description page under the help tab (assuming you are using RStudio).

## Installing the package from CRAN

Installing the package from CRAN for developing purposes is not recommended. Because most probably, the version on CRAN is not the latest version.

[Complete this section after submitting the package to CRAN]

## Installing the package from the source

In order to install the package from the source, you need to download the source code into your computer and install it from the source. Here are the steps:

• Go to package Github repository and from the drop-down menu change the branch to develop. Then click on the Code tab and then click on the Download Zip tab.

• Open one of the files using RStudio, then change the project directory to the project directory (Session > Set Working Directory > To Project Directory).

• Load devtools library and then load CRE.

library(devtools)
?CRE

## Forking the package

Forking the package under your Github account is the best option if you are planning on installing, testing, modifying, and contributing to the project. Go to package Github repository and click on the Fork button at the top right corner. After forking the package, Open your terminal (or Gitbash for Windows, Anaconda prompt, …) and run the following command (brackets are not included):

git clone git@github.com:[your user name]/CRE.git

Now, you can modify the codebase and track your modification. Navigate to the package folder and Install the package following the Installing the package from source steps. It is a good idea to create a new branch to work on the codebase. Read A successful Git Branching Model for branching convention.

# Testing the Package

Run the following command to test the package.

library(CRE)

# Generate sample data
set.seed(1358)
dataset <- generate_cre_dataset(n = 1000,
rho = 0,
n_rules = 2,
p = 10,
effect_size = 2,
binary_covariates = TRUE,
binary_outcome = FALSE,
confounding = "no")
y <- dataset[["y"]]
z <- dataset[["z"]]
X <- dataset[["X"]]

method_params <- list(ratio_dis = 0.25,
ite_method_dis = "aipw",
include_ps_dis = TRUE,
ps_method_dis = "SL.xgboost",
ps_method_inf = "SL.xgboost",
oreg_method_dis = "SL.xgboost",
oreg_method_inf = "SL.xgboost",
ite_method_inf = "aipw",
include_ps_inf = TRUE,
offset = NULL)

hyper_params <- list(intervention_vars = NULL,
ntrees_rf = 200,
ntrees_gbm = 200,
node_size = 20,
max_nodes = 5,
max_depth = 15,
replace = TRUE,
max_decay = 0.025,
type_decay = 2,
t_ext = 0.01,
t_corr = 1,
t_pvalue = 0.05,
stability_selection = TRUE,
cutoff = 0.6,
pfer = 1,
penalty_rl = 1)

# linreg CATE estimation with aipw ITE estimation
cre_results <- cre(y, z, X, method_params, hyper_params)
summary(cre_results)
plot(cre_results)


text:
# Y=-5x-1

Find the slope of the line y=-5x-1.

The equation y = -5x-1 is already in slope-intercept form.

Slope-Intercept Form:  y = mx + b

m = the slope of the line

b = the y-intercept (where the line crosses the y-axis)

So, the slope of the line is -5 and it crosses the y-axis at -1.

Approved by eNotes Editorial Team

Find the slope of the line `y= -5x-1` .

The equation is written in slope-intercept form: `y =mx+b` , where `m` represents the slope and `b` represents the y-intercept.

Therefore, -5 is the slope and -1 is the y-intercept.

The solution for the slope of the line is -5.

Approved by eNotes Editorial Team

This equation is in the slope-intercept form

y=mx+b

where m is the slope and b is the y intercept.

In the linear equation y=-5x-1, the slope is -5 and the y intercept is -1.

Here is the graph:

Approved by eNotes Editorial Team

format: plain


text:
# Matrix Multiplication

Matrix multiplication of "m by n matrix" $A_{m\text{x}n}$ by "p by q matrix" $B_{p\text{x}q}$ can be defined exactly when the dimensions n and p are equal. (It doesn't make sense otherwise.)

The concise (and possibly confusing) "symbolic" definition defines the product of an "m by n matrix" $A_{m\text{x}n}$ and a "n by q matrix" $B_{p\text{x}q}$ (written P=AB) is given entry by entry as

$P_{ij}=\sum_{k=1}^{n}(A_{mk}*B_{kq})$.

In other words, to calculate a specific number in row r and column c in AB, look only at the row r in A, and in column c in B. Then multiply the first number in A's row by the first number in B's column, and the second number in B's row by the second number in B's column, and so on. Finally, add these all up to get that specific number in the product matrix.

For example, to mutliply the first matrix A by the second matrix B, consider only one row and column at a time:

$\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \times \begin{bmatrix} 4 & 6 & 9\\ 2 & 3 & 5\\ 7 & 8 & 1\end{bmatrix}$

By multiplying a 2 by 3 matrix with a 3 by 3 matrix, the result will be a 2 by 3 matrix. To get the entry in the second row and first column of the product, consider only the second row in A, and the first column in B.

$\begin{bmatrix} ? & ? & ? \\ 4 & 5 & 6 \end{bmatrix} \times \begin{bmatrix} 4 & ? & ?\\ 2 & ? & ?\\ 7 & ? & ?\end{bmatrix} =\begin{bmatrix} ? & ? & ? \\ 68 & ? & ?\end{bmatrix}$

Because $4*4+5*2+6*7=68$, that entry is 68. This can be repeated for all 6 entries to find the product.

Keep in mind that matrix multiplication depends on the order the matrices are multiplied; computing AB is usually not the same as BA. This means matrix multiplication is not commutative.


text:
# fit a curve in a three dimensional space

I have a list of points of a curve in a three dimensional space, like

myData =
{{1.6251942652167208, 3414.632234882431, 3.248326448352207},
{0.195563463104691, 32.18966154343482, 1.1454060351007385},
{0.17904199044243319, 14.25108939238815, 0.9423477799753123},
{0.170816821901991, 8.653164633472851, 0.7958880823665402},
{0.15676037756308206, 5.631156542779637, 0.67467521725227},
{0.1548948722263085, 4.270874169070245, 0.6275611866853114},
{0.1876950201556172, 4.308999312640106, 0.6090637255823652},
{0.16188251254916763, 2.9764924022024317, 0.5292892925723116},
{0.17262610022897934, 2.739111371641244, 0.52653513586836},
{0.16954431585785373, 2.3070638999549393, 0.49560804724631763},
{0.2097961985882085, 2.6534757543854317, 0.5487657657669014},
{0.19081633352127408, 2.0852454796400357, 0.514435548916157},
{0.19563129613920563, 1.917093872159669, 0.4743406166681895},
{0.21254024573386504, 1.9251337728677473, 0.485236735240245},
{0.21896472970440534, 1.8147535334973488, 0.46531629302089494},
{0.20466136180653818, 1.513876366963674, 0.4249037110237554},
{0.21855394267841366, 1.519108716384235, 0.4380750296933395},
{0.23565318703002316, 1.5488572100526539, 0.44631964709969185},
{0.2380818528018018, 1.4529671243699986, 0.42553379428103266},
{0.2424842011874948, 1.389721482236748, 0.4345346021692877},
{0.2647317878191315, 1.4605691656957687, 0.43267419256049483},
{0.2632502748033041, 1.3557447019366855, 0.4286184053606104},
{0.27205729604073775, 1.334394688581283, 0.44259414855715523},
{0.2793705082711959, 1.302387809445032, 0.4336404208867536},
{0.2837573939406187, 1.2544604741697558, 0.42970441420505734},
{0.2948407139307023, 1.251503834903687, 0.4289108411034688},
{0.29600086351343347, 1.1920618765471473, 0.42889878404407833},
{0.29465197778349606, 1.1243426155800962, 0.4276172983591667},
{0.30183374846249794, 1.1064964396078605, 0.42772557494175767},
{0.30918455260251276, 1.0893160114201885, 0.4275101914583863},
{0.3170183678910846, 1.0761991260380923, 0.4251450946217794},
{0.3170471652361686, 1.028070998453355, 0.4231589533788725},
{0.33509119696542056, 1.062744456154385, 0.4233345521815623},
{0.32971337187673616, 0.9954325606304446, 0.4231326015290622},
{0.33595705730728015, 0.979557033300735, 0.4236769992893109},
{0.3436253098086924, 0.9714372846864234, 0.4241910609852374},
{0.34812463781047914, 0.949934939902976, 0.42012852465803996},
{0.3563732253707738, 0.9443465112229241, 0.4204752685781463},
{0.35992684291158533, 0.9221331266260643, 0.41804460944990646},
{0.36120796960334306, 0.893126929139083, 0.41819781912012344},
{0.3694695389695183, 0.8578713443146384, 0.4150160053145223},
{0.37334083248099226, 0.8414330588993054, 0.4145221485938744},
{0.3766063600562105, 0.8812611721272469, 0.45266007028291844},
{0.3835672074215254, 0.8426364383173903, 0.44224264257818485},
{0.3925576360242645, 0.8145071347303069, 0.441619765516166},
{0.3952083972535039, 0.7698172682169502, 0.4289584794098478},
{0.40767794715674194, 0.7561905560105875, 0.42830082380993906},
{0.4139609495348973, 0.7284690866030674, 0.42802517746189234},
{0.4199909107710205, 0.7017646393366863, 0.4245332938666336},
{0.42517695763043706, 0.6756040929172838, 0.41901542028878747},
{0.438909457948436, 0.6699655678281783, 0.41733783818556264},
{0.44563579799220726, 0.6499029238980055, 0.4129281969548992},
{0.4473498530318954, 0.6211332659501384, 0.4089614451608291},
{0.45464041389498117, 0.6051969313774956, 0.4050849964713832},
{0.46156953220721025, 0.5899702211293141, 0.4029806473833252},
{0.47141055300556484, 0.5805373200701324, 0.39970427922756985},
{0.4792326437523886, 0.5681016242905145, 0.39694835543120627},
{0.4853330654106727, 0.553725319161017, 0.393182829103135},
{0.49135512137375686, 0.5399417830238199, 0.3901371989617769},
{0.5006324150392757, 0.5320562690230357, 0.3875692692973447},
{0.5064951595246885, 0.5194105475320817, 0.3832282043244645},
{0.5115547319598217, 0.5062662671288428, 0.3811347260859499},
{0.51504804958564, 0.4917529304140576, 0.3775795425712839},
{0.5220718511737211, 0.48266019418477496, 0.37470445520090895},
{0.5312779766503062, 0.47705149397591645, 0.37098468508988963},
{0.5324554882538403, 0.4612891859386048, 0.36767364179185347},
{0.5377840374755473, 0.451700594900957, 0.3651018926671713},
{0.5450134070805016, 0.44432218995571343, 0.3621032659850748},
{0.5532192176564933, 0.438742917967833, 0.35988610407498006},
{0.5559200803701375, 0.4272035754877022, 0.3562923772639558},
{0.5632612273324766, 0.42125311233985596, 0.35442749937954365},
{0.5695771900612702, 0.4143325143071145, 0.35207878660073166}}

I want to find and plot a find of this curve in the space.

I don't have a explicit form of the real function, but I know that it is regular enough to allow a polynomial expansion in the interval of interest.

Is this possible?

If you don't have a clue about the underlying model of your data, why don't you interpolate it then?

With[{ip = ListInterpolation[#, {{0, 1}}] & /@ Transpose[myData]},
func[t_] := Through[ip[t]]
];

ParametricPlot3D[func[t], {t, 0, 1}, BoxRatios -> 1]

With this you have a function and you can evaluate your curve everywhere inside the defined interval.

• sorry, I was inaccurate. I indeed have equations for that curve, but are so complex that I can't get an explicit form to fit. I know that the curve is indeed very regular in that interval, and a polynomial expansion is surely possible. Nevertheless I do not know how many terms I need to include in the fit, but in my case I have other fixed point in that space, so I can get the accuracy of the result a posteriori. Oct 21, 2013 at 12:21
• @Fabrizio What "other fixed point" do you have? Oct 21, 2013 at 14:07
• @belisarius I have two points (with much more accuracy) that I know must belong to the curve, but I don't want necessarily include them in the fit, because are obtained with a different method. But because they are far enough apart, I can use them to evaluate in some sense the accuracy of the fit. Oct 21, 2013 at 18:20
• @Fabrizio But you should include them in your question. It's the only way to let us check the fit ... Oct 21, 2013 at 18:33
• @belisarius I partially disagree. I asked just for a good fit of that list of points, that it is in general different from a good fit of the underlying model (and that it's not part of my question). Oct 21, 2013 at 18:42

I am not sure I understand what the problem is with @hairutan's answer. If you want to visually inspect the data and select a model to fit it based on the model not being too complex (rather than the goodness of the fit), you can find a parametric curve that does that by fitting each dimension separately and experiment how many terms to include in each dimension.

p[order1_, order2_, order3_] := Block[{f1, f2, f3, model},
model[order_] := Flatten@Table[{x^n, x^(-n)}, {n, 0, order}];
f1 = Fit[myData[[All, 1]], model[order1], x];
f2 = Fit[myData[[All, 2]], model[order2], x];
f3 = Fit[myData[[All, 3]], model[order3], x];
{f1, f2, f3}];

Here, I've added negative powers to improve the fit.

Manipulate[
TableForm@{Show[{ListPointPlot3D[myData, PlotRange -> All,
PlotStyle -> Directive[{Red, PointSize[.015]}]],
ParametricPlot3D[
Evaluate@p[n1, n2, n3], {x, 1, Length[myData]},
PlotStyle -> Thick]},
BoxRatios -> 1, PlotRange -> All],
"{n1,n2,n3}=" <> ToString@{n1, n2, n3}},
{n1, 1, 6, 1}, {n2, 1, 6, 1}, {n3, 1, 6, 1}]

After some experimentation p[3,4,3] seems to fit OK:

but I think that's deceptive (owing to the aspect ratio of the box etc). In fact, The difference in variance between columns of your data suggests you may want to take their logarithm before fitting. In any case, unless you give a little more on what model you expect I can't see how any answer will be better than ListInterpolation (unless someone finds a way to do something really fancy)

• the problem with @hairutan's answer it's that it is incomplete and I misunderstood his hint. Your answer made it clear to me, and yes, it's enough to solve my problem. Oct 21, 2013 at 18:35


text:
## [ Politics ] Open question: W Bush barely won in 2000, but with a strong economy, he won 12 million votes and won a landslide in 2004. Will history repeat itself with Trump?

[Politics] Open question: W Bush barely won in 2000 but with a strong economy won 12 million votes and won a landslide in 2004. Will history repeat itself with Trump?

## tracing – high r square but strong residue pattern

I analyze the evolution of the total number of users over time. It is obvious that a linear regression corresponds to the data. The r squared is then also 0.9961.

Now the problem: a trace of the residues shows the presence of a pattern. This should not be the case if the model was correct.

Does anyone have experience in solving this problem? I tried adjusting the time series model, which gave me a random walk model (ARIMA 0.1,0) but I am unable to find the coefficients of this model, which is exactly what I need.

Thank you.

## bip 32 hd wallets – Why can't a strong xpub key generate a public child key?

Uncured parents effectively use the public key to derive their children, where hardened parents derive their children from the private key.

Deriving a child private key from an unenforced parent private key `k` uses the following hash function:

``````HMAC-SHA512(chainCode, point(k) || i)
``````

We know that `K = point(k)`, or `K` is the parent public key. So if we only know `K` and not necessarily `k`, we can always derive the child key by replacing `point(k)` with `K`and follow the normal process.

With reinforced private keys, hashing is done differently:

``````HMAC-SHA512(chainCode, 0x00 || k || i)
``````

Here you can see that there is no way to calculate this hmac without knowing it `k`. Just know the public key `K` will not help.

It looks like you should be using the `deriveHardened` operate in bitcoinjs rather than in clear `derive`.

## lo.logic – How strong is the consistency of adding this ordinal reflection pattern on top of Ackermann's set theory?

Axiomatic diagram of ordinal reflection: if $$phi$$ is a formula that does not use the symbol $$V$$, whose parameters are among $$x_1, .., x_n$$; then: $$forall x_1 in V, dotsc, forall x_n in V: phi (On) to \ forall c subseteq On \ (c = { alpha in On | phi ( alpha) } lor bigcup (c) = On to | c | = On);$$ is an axiom.

Or: $$On = { alpha in V | operatorname {ordinal} ( alpha) };$$ and "$$| c |$$"means class cardinality $$c$$, defined as the least von Neumann ordinal class bijective to $$c$$.

Add this axiom on top of Ackermann's set theory.

How strong would the resulting theory be?

## lo.logic – How strong is the consistency of adding this ordinal reflection pattern on top of Ackermann's set theory?

Axiomatic diagram of ordinal reflection: if $$phi$$ is a formula that does not use the symbol $$V$$, whose parameters are among $$x_1, .., x_n$$; then: $$forall x_1 in V, .., forall x_n in V: phi (On) to \ forall c subseteq On \ (c = { alpha in On | phi ( alpha) } lor bigcup (c) = On to | c | = On)$$; is an axiom.

Or: $$On = { alpha in V | ordinal ( alpha) }$$; and $$“ | c | "$$ means class cardinality $$c$$, defined as the least von Neumann ordinal class bijective to $$c$$.

Add this axiom on top of Ackermann's set theory.

How strong would the resulting theory be?

## Why is the economy so strong? I remember that Trump being elected would mean recession and disaster?

It's just the dream of the Democrats, as America enters recession. Set aside the fact that Trump has produced one of the largest stock markets in history; The GDP is way above Obama or Jimmy Carter, both of whom have produced disastrous economies that have almost destroyed the middle class; 3.5% unemployment is the lowest in 50 years; as many Americans work in history; and unemployment among blacks and Latinos is the lowest in history.

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text:
# When to include chemical potential in Gibbs equations?

I'm struggling to understand when to and when not to include the chemical potential in the differential forms of the thermodynamic potentials. In principle I would assume that any system wherein the number of particles or the composition is changing should include the term - however I have run into two issues.

1. Whilst studying thermochemistry, my lecturer was quick to bring up some old results from thermodynamics, that the heat of an isobaric process corresponds to the enthalpy change and the heat of an isochoric process corresponds to the internal energy change.

A quick 'derivation' shows this : $$dH=TdS+VdP$$ which at constant pressure becomes $$dH=TdS=q_P$$ however, had we included the chemical potential we would have obtained $$dH=TdS+\sum_i\mu_idn_i=q_P+\sum_i\mu_idn_i$$Thus when interpreting $$\Delta H$$ as heat of reaction under constant pressure, are we not ignoring the effects of composition on H?

1. Earlier, when chemical potential was first being introduced in my Pchem class - a derivation of the condition of spontaneity for transport between phases was put forward:$$dG=-SdT+VdP+\sum_i\sum_j\mu_i^jdn_i^j$$ and from the second law we know that for an irreversible process $$dG<-SdT+VdP$$, thus: $$\sum_i\sum_j\mu_i^jdn_i^j<0$$ However, I would argue that this formulation of the second law is not accurately accounting for chemical potential. Consider the more general $$TdS\geqq dq$$, and the first law $$dU=dq+dw$$, one obtains that $$dG\leqq VdP-SdT+w_{non-PV}$$ which to reproduce the first equation in the case of a reversible proces, I would identify that $$w_{non-PV}=\sum_i\sum_j\mu_i^jdn_i^j \rightarrow dG\leqq -SdT+VdP+\sum_i\sum_j\mu_i^jdn_i^j$$ Of course with this result you can no longer figure out the condition of spontaneity this way as you simply get $$0<0$$. Furthermore wouldn't the lecturer's original derivation technically be applying both a relation that holds specifically for reversible processes and one for irreversible processes together? When it came to entropy as a condition for spontaneity in isolated systems - we knew that only reversible or irreversible pathways existed between two states but not both, preventing such potential contradictions. Though I'm uncertain if a similar interpretation can be made for the formulation in terms of Gibbs energy.

Am I merely confusing myself with the interpretation of chemical potential as a form of non-PV work?

1. You are assuming $$T\text{d}S =\delta Q$$, which is only true if the process is internally reversible; in fact, the other expression, $$\delta Q_P = \text{d}H_P$$, is the general one, as it can be derived directly from the first law for an isobaric process with no "other" work: \begin{align} \text{d}U &= \delta Q - P \text{d}V - \delta W_\text{other}^\text{out} \\ \text{d}U_P &= \delta Q_P - P \text{d}V_P - \underbrace{\delta W_\text{other}^\text{out}}_0 \\ \text{d}U_P + P \text{d}V_P &= \delta Q_P \\ \text{d}H_P &= \delta Q_P \end{align} This expression holds for a closed system undergoing a process with no non-mechanical work or acceleration regardless of whether or not there are chemical reactions.
2. You seem to be confusing expressions for $$W_\text{non-PV}$$ with extremum principles which are derived for the special case where $$W_\text{non-PV}$$ is fixed as zero.

Earlier, when chemical potential was first being introduced in my Pchem class - a derivation of the condition of spontaneity for transport between phases was put forward:$$dG=-SdT+VdP+\sum_i\sum_j\mu_i^jdn_i^j$$

This is true in general.

and from the second law we know that for an irreversible process $$dG<-SdT+VdP$$, thus: $$\sum_i\sum_j\mu_i^jdn_i^j<0$$

This is only true in the special case where $$W_\text{non-PV} = 0$$. Combining these results will just lead to the conclusion $$W_\text{non-PV}= 0$$, which was the starting point.

Relationship between Chemical Potential and "Other" Work

Am I merely confusing myself with the interpretation of chemical potential as a form of non-PV work?

It seems that you are. Although it is generally true that $$\delta W_\text{mechanical} = P\text{d}V$$, it is not generally true that $$\delta W_\text{other} = \sum_i \mu_i \text{d}n_i$$.

The first law connects fluxes across the system boundary to property changes within the system; "other" work is a flux, while the chemical potential term is a property change: \begin{align} \overbrace{\delta Q \underbrace{- P\text{d} V - \delta W_\text{other}}_{-\delta W}}^\text{\text{d}U in terms of fluxes} &= \overbrace{T\text{d}S - P\text{d}V + \sum_i \mu_i \text{d}n_i}^\text{\text{d}U in terms of properties} \end{align}

I imagine that you are thinking that $$\delta W_\text{other}$$ must equal $$\sum_i \mu_i \text{d}n_i$$ in order to be able to derive the Gibbs Equation, but this is not the case - they aren't equal, and the Gibbs Equation is derived in a different way.

Deriving the Gibbs Equation from the First Law

The easiest way I know to derive the Gibbs Equation for $$U$$ from the First Law is to consider a process in which $$\delta W_\text{other} = 0$$ and the composition is changed by reversibly adding/removing chemical components rather than by chemical reactions (diffusion becomes reversible in the limit where the driving concentration gradient approaches zero, just as heat transfer becomes reversible in the limit where the temperature gradient approaches zero). Since this process is reversible, we can say $$\delta Q = T \text{d}S$$. If we define the chemical potential of species $$i$$, $$\mu_i$$, as $$\mu_i \equiv \left( \frac{\partial U}{\partial n_i} \right)_{S,V,n_{j\neq i}}$$ then we can conclude that total $$U$$ added to the system by mass transfer in this model process is $$\sum_i \mu_i \text{d}n_i$$, and thus $$\text{d}U_\text{model process} = \underbrace{T \text{d} S}_\text{Heat} - \underbrace{P \text{d} V}_\text{Work} + \underbrace{\sum_i \mu_i \text{d} n_i}_\text{Mass Transfer}$$ Since $$U$$ is a property (as opposed to a flux), changes in $$U$$ depend only on the initial and final states (not on the path between them), so we can conclude that for any arbitrary process - even one involving "other" work or chemical reactions - the expression $$\text{d}U = T \text{d} S - P \text{d} V + \sum_i \mu_i \text{d} n_i$$ continues to hold. Note that the labelling of the individual terms as heat, work, and transfer by mass is specific to the model process; in general, we can't identify the individual terms in the equation with fluxes - we can just identify the sum of the terms with the sum of the fluxes.

• Many thanks for your answer! 1. My problem here id that to derive $dH_p=\delta Q_p$ as you did, one must assume that only PV work is significant. But isn't composition change another way to alter the energy of the system and therefore another form of 'work'? Else, what about a chemical reaction between ideal gases at constant temperature and volume, where I reversibly add heat to the system to drive an endothermic reaction forward? Under these conditions: $\Delta U=0, W=0$. So where is the heat going? Shouldn't it be going into changing the chemical potential? Jun 10, 2019 at 8:01
• Chemical potential isn't a work mode - it's more of a way that the system can store energy. In your example, $\Delta U \neq 0$ - you are heating the system, so the first law says $\Delta U > 0$ (I assume you were thinking that $\Delta T = 0$ implies $\Delta U = 0$, but this is only true for a pure substance - i.e. if there are no chemical reactions). If there are endothermic chemical reactions but $T$ is constant, then the system will store the energy as chemical potential without changing $T$. Jun 10, 2019 at 19:52
• I was going on the notion that $\Delta T=0$ implies $\Delta U=0$ for Ideal gases. But, I see what you are saying. This condition comes from analysis of pure substance systems. My confusion remains, however. If chemical potential cannot be taken to be work, how can one write $dU = \delta Q - PdV - \delta W_{other}$ without considering energy being stored as chemical potential? shouldn't the more general form be $dU = \delta Q - PdV - \delta W_{other} + \sum_i \mu_i dn_i$? This reduces to $dU = TdS - PdV + \sum_i \mu_i dn_i$ for a reversible process, which is the Gibb's equation for U. Jun 11, 2019 at 0:11
• I've edited my response to address your last comment Jun 11, 2019 at 1:45
• Thanks a lot! With that explanation I think I finally understand. I was getting hung up on trying to identify each term on the Gibbs equation for U with a flux, but the Gibbs equation is fundamentally a differential expansion of U strictly in terms of properties and not fluxes as you said. It seems so obvious now that there need not be a one-to-one correspondance with the expression of dU in terms of fluxes (from the first law). I'm sorry that it took this much for me to get it, but really thank you for guiding me through it! Jun 11, 2019 at 12:35


text: Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. Exception: Peroxides. Oxidation/reduction reaction-metal/nonmetal reaction (sometimes nonmetals undergo ox/red if oxygen is a reactant) 2Na(s)+Cl2(g) 2NaCl(s) Na + Cl Na++ Cl-oxidation reduction Is it illegal to carry someone else's ID or credit card? It is known to dissociate into barium cations and chloride anions in its dissolved state. How can one plan structures and fortifications in advance to help regaining control over their city walls? How can I discuss with my manager that I want to explore a 50/50 arrangement? By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. The oxidation number of a simple ion is the charge of the ion. The oxidation number for hydrogen in most compounds is +1. What is the oxidation number of barium and chlorine in BaCl2? At a temperature of 20 oC, the solubility of barium chloride in water is roughly equal to 358 grams per litre. The oxidation number of oxygen in most compounds is -2. Can the automatic damage from the Witch Bolt spell be repeatedly activated using an Order of Scribes wizard's Manifest Mind feature? Chemistry. Barium chloride is quite soluble in water (as is the case with most ionic salts). How to assign oxidation number of sulfur in thiocyanate anion? The oxidation number of a monatomic ion equals the charge of the ion. Want to improve this question? Barium is a metal that exhibits an oxidation state of +2 in this ionic salt whereas chlorine is a non-metal which exhibits an oxidation state of -1 in BaCl2. Answer to: Which of the following chemical reactions is an oxidation-reduction reaction? 4. which reactant ba or hcl got oxidized? Ingestion or inhalation of barium chloride can also prove fatal. Required fields are marked *, Barium chloride is quite soluble in water (as is the case with most ionic salts). It is known to dissociate into barium cations and chloride anions in its dissolved state. This compound is also soluble in methanol (however, it is not soluble in ethanol). In a redox reaction, how does the total number of electrons lost by the oxidized substance compare to the total number of electrons gained by the reduced substance? Barium Chloride is used as a raw material to produce barium salt. Chlorine can be used instead of hydrochloric acid. (2) The number lost is always equal to the number gained. 2AgNO3 (aq) + BaCl2 (aq) 2AgCl(s) + Ba(NO3)2 (aq) b. Ag2+ (aq) + 2Cl- (aq) AgCl2 (s) c. Ag+ (aq) + Cl- (aq) AgCl (s) d. Ba2+ (aq) + 2NO3- (aq) Ba(NO3)2 (aq) e. none of these 3. assign oxidation numbers to the reactants and products in rhe net ionic equation. Learn more about the physical and chemical properties of Barium Chloride (BaCl2) from the experts at BYJUâS. I accidentally added a character, and then forgot to write them in for the rest of the series. BaSO4 is comparatively non-toxic due to its insolubility. Setters dependent on other instance variables in Java. 5. which reactant ba or hcl got reduced. Oxidation-loss of electrons. According to redox rules, column 2 elements (alkali earth metals) have an oxidation number of +2, but in this reaction: $\ce{Ba + Cl2 -> BaCl2}$, the oxidation number of $\ce{Ba}$ changes from $0$ on the left to $+2$ on the right instead of starting from $0$ on the left. The rules that you are referring to are for atoms in compounds, not in pure elements. The alkali metals (group I) always have an oxidation number â¦ According to redox rules, column 2 elements (alkali earth metals) have an oxidation number of +2, but in this reaction: $\ce{Ba + Cl2 -> BaCl2}$, the oxidation number of $\ce{Ba}$ changes from $0$ on the left to $+2$ on the right instead of starting from $0$ on the left. Magnesium sulfate (MgSO4) and Sodium sulfate (Na2SO4) are probable antidotes as they form BaSO4 (barium sulfate). At a temperature of 100 oC, the solubility of barium chloride in water is equal to 594 grams per litre. It is used in chlorine-alkali industries. Since is in column of the periodic table , it will share electrons and use an oxidation state of . C, the solubility of barium chloride in water is equal to 594 grams per litre. Why does a chemical have more than one oxidation number? Why do most Christians eat pork when Deuteronomy says not to? Rules for assigning oxidation numbers. Barium Chloride is an inorganic saltÂ that is made up of barium cations (Ba+) and chloride anions (Cl–). Barium chloride molecules feature an ionic bond between barium cations and chloride anions. According to rule 4, the sum of the oxidation number on all atoms must equal the charge on the species, so we have the simple algebraic equation. In $\ce{BaCl2}$ the oxidation state of barium is +2 and the oxidation state of chlorine is -1. Is it possible to just construct a simple cable serial↔serial and send data from PC to C64? Under standard conditions, barium chloride exists as a white crystalline solid (as shown above). It only takes a minute to sign up. If Jedi weren't allowed to maintain romantic relationships, why is it stressed so much that the Force runs strong in the Skywalker family? Considering these separately, the Ba 2+ ion has an oxidation number of +2 by rule 2. However, the dihydrate form of barium chloride is known to have a monoclinic crystal structure. Then, the barium sulphide is treated with hydrochloric acid to yield barium chloride along with hydrogen sulphide. Can you use the Eldritch Blast cantrip on the same turn as the UA Lurker in the Deep warlock's Grasp of the Deep feature? Now consider the NO 3 â ion. Reduction-gain of electrons. Plausibility of an Implausible First Contact. Your email address will not be published. Anhydrous BaCl2 crystallizes in an orthogonal crystal structure. Barium salts are extensively used in the industry. Is it ok for me to ask a co-worker about their surgery? O +6 O-1 O +1 O +5 In Which Reaction Is Carbon Reduced? However, the solubility of this compound in water is temperature-dependent. Â It is also called Barium Muriate or Barium dichloride. First, barium sulfate (usually in the form of the mineral barite) is reacted with carbon at high temperatures to form barium sulphide and carbon monoxide. ... + Ba(OH)2(aq) +2H2O(l) + BaCl2(aq) What is the molar concentration of the barium hydroxide solution? [closed], MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…, “Question closed” notifications experiment results and graduation. What Is The Oxidation Number Of Nitrogen In The Nitrate Ion? The oxidation number of Ba is +II, and the oxidation number of each of the oxygens in the peroxide anion is -I. What is the oxidation number of the oxygen in BaO2, Determine the oxidation number of sulfur in SF6. When exposed to sulfates, a white precipitate of barium sulfate is obtained. Since $\ce{BaCl2}$ is also a binary ionic compound, these oxidation states correspond to the charges on the ions: $\ce{Ba^2+}$ and $\ce{Cl-}$. Barium chloride is poisonous in nature. At a temperature of 20, C, the solubility of barium chloride in water is roughly equal to 358 grams per litre. Integral solution (or a simpler) to consumer surplus - What is wrong? Anhydrous BaCl. Alkaline earth metals have oxidation state of +2 when they are combined with nonmetals in compounds, such as in $\ce{BaCl2}$. Step 1: From barium sulfate at high temperature. Your email address will not be published. 1. write thw ionic equation for ba+2hcl=bacl2+h2. This compound has limited applications due to its high toxicity. Oxidation number (also called oxidation state) is a measure of the degree of oxidation of an atom in a substance (see: Rules for assigning oxidation numbers). Given redox reaction is, Ba(s) + 2HCl(aq)BaCl2(aq) + H2(g) oxidation state of Ba(s) = 0 oxidation state of hydrogen ion in HCl (aq) = +1 oxidation state of chlorid view the full answer (1) The number lost is always greater than the number gained. Why does Pb normally have an oxidation number of +2? rev 2020.12.2.38097, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Why is oxidation number of Ba not +2 in this case? 2. write the net ionic equation for the same reaction as above. Yes, like most other salts of barium, BaCl2 is highly toxic to human beings. Is it worth getting a mortgage with early repayment or an offset mortgage? I accidentally used "touch .." , is there a way to safely delete this document? However, the dihydrate form of barium chloride is known to have a monoclinic crystal structure. The sulfate is used in white paints, particularly for outside use. Oxygen is assigned an oxidation number of â2, and there are three oxygens. It is a white solid which is water-soluble, hygroscopic and gives a slight yellow-green colour to a flame. Under standard conditions, barium chloride exists as a white crystalline solid (as shown above). 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Ca 0 + Cl 0 2 â Ca +2 Cl -1 2 b) Identify and write out all redox couples in reaction. Question: What Is The Oxidation Number Of Nitrogen In The Nitrate Ion? Aqueous solutions of barium chloride have neutral pH values since they contain the cation of a strong base and the anion of a strong acid. Exposure to this compound can cause irritation of the eyes, mucous membrane, and skin. Find the Oxidation Numbers BaSO_4 Since is in column of the periodic table , it will share electrons and use an oxidation state of . Fluorine in compounds is always assigned an oxidation number of -1. This compound is also soluble in methanol (however, it is not soluble in ethanol). Industrially, it is obtained in two steps. Converting 3-gang electrical box to single. Barium chloride can also negatively impact the central nervous system, the cardiovascular system, and the kidneys. This compound is toxic when ingested. Building algebraic geometry without prime ideals. The industrial production of barium chloride follows a two-step process. crystallizes in an orthogonal crystal structure. The chemical formula of Barium Chloride is BaCl2. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Ubuntu 20.04: Why does turning off "wi-fi can be turned off to save power" turn my wi-fi off? Why isn't hydration an oxidation reaction? On the left side of the equation, barium and chlorine are present in their elemental form, and, by definition, both have oxidation state of 0. Barium chloride molecules feature an ionic bond between barium cations and chloride anions. Choose the correct net ionic equation for the reaction in water of AgNO3 and BaCl2. Why is this? 6. which reactant ba hcl is the oxodazing agent ? how can we remove the blurry effect that has been caused by denoising? (3) The number lost is sometimes equal to the number gained. The oxidation number of a free element is always 0. The primary industrial application of BaCl2 is in the purification of the brine solutions that are used in caustic chlorine plants. This fits with the charge of the peroxide anion ($2 \times -1 = -2$), and as $\ce{BaO2}$ is a neutral compound, the sum of all oxidation numbers is 0. Add details and clarify the problem by editing this post. Why is the following reaction not considered a redox reaction? a. At a temperature of 100. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. However, the solubility of this compound in water is temperature-dependent. 1 Answer anor277 Dec 15, 2017 It can also be obtained from barium carbonate or barium hydroxide. Barium is a metal that exhibits an oxidation state of +2 in this ionic salt whereas chlorine is a non-metal which exhibits an oxidation state of -1 in BaCl2. 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In pure elements in rhe net ionic equation â it is also soluble in methanol however. O +5 in which reaction is Carbon Reduced me to ask a co-worker their.


text:
# generating function / stream cipher

I'm struggling to solve this exercise.

$s_n = 6s_{n-1} - 5s_{n-2}$ with initial states $s_1 = 1$ and $s_2 = 2$

Now I have to find a closed formula for this sequence.

The generating function is given by $f(z) = \frac{s_1}{z} + \frac{s_2}{z^2} + ...$

How can I find from this the generating function with $z^2 - 6z + 5$ in the denominator? Thanks for any hints.

• Why not $f(z)=s_1z+s_2z^2+s_3z^3+\cdots$? – Lord Shark the Unknown Jan 31 '18 at 18:12
• we definded it the other way and have to do it like this. – Livpez. Jan 31 '18 at 18:19

Since $$s_{n+2}-s_{n+1}=5(s_{n+1}-s_n),$$ we obtain $$s_{n+1}-s_n=5^{n-1}$$ and use the telescopic sum.
I got $$s_n=\frac{5^{n-1}+3}{4}.$$


text:
10.11 Cohesion and adhesion in liquids: surface tension and capillary  (Page 6/11)

 Page 6 / 11

How does sap get to the tops of tall trees? (Recall that a column of water can only rise to a height of 10 m when there is a vacuum at the top—see [link] .) The question has not been completely resolved, but it appears that it is pulled up like a chain held together by cohesive forces. As each molecule of sap enters a leaf and evaporates (a process called transpiration), the entire chain is pulled up a notch. So a negative pressure created by water evaporation must be present to pull the sap up through the xylem vessels. In most situations, fluids can push but can exert only negligible pull , because the cohesive forces seem to be too small to hold the molecules tightly together. But in this case, the cohesive force of water molecules provides a very strong pull. [link] shows one device for studying negative pressure. Some experiments have demonstrated that negative pressures sufficient to pull sap to the tops of the tallest trees can be achieved.

Section summary

• Attractive forces between molecules of the same type are called cohesive forces.
• Attractive forces between molecules of different types are called adhesive forces.
• Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called surface tension.
• Capillary action is the tendency of a fluid to be raised or suppressed in a narrow tube, or capillary tube which is due to the relative strength of cohesive and adhesive forces.

Conceptual questions

The density of oil is less than that of water, yet a loaded oil tanker sits lower in the water than an empty one. Why?

Is surface tension due to cohesive or adhesive forces, or both?

Is capillary action due to cohesive or adhesive forces, or both?

Birds such as ducks, geese, and swans have greater densities than water, yet they are able to sit on its surface. Explain this ability, noting that water does not wet their feathers and that they cannot sit on soapy water.

Water beads up on an oily sunbather, but not on her neighbor, whose skin is not oiled. Explain in terms of cohesive and adhesive forces.

Could capillary action be used to move fluids in a “weightless” environment, such as in an orbiting space probe?

What effect does capillary action have on the reading of a manometer with uniform diameter? Explain your answer.

Pressure between the inside chest wall and the outside of the lungs normally remains negative. Explain how pressure inside the lungs can become positive (to cause exhalation) without muscle action.

Problems&Exercises

What is the pressure inside an alveolus having a radius of $2\text{.}\text{50}×{\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{m}$ if the surface tension of the fluid-lined wall is the same as for soapy water? You may assume the pressure is the same as that created by a spherical bubble.

$\text{592}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$

(a) The pressure inside an alveolus with a $2\text{.}\text{00}×{\text{10}}^{-4}$ -m radius is $1\text{.}\text{40}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{Pa}$ , due to its fluid-lined walls. Assuming the alveolus acts like a spherical bubble, what is the surface tension of the fluid? (b) Identify the likely fluid. (You may need to extrapolate between values in [link] .)

What is the gauge pressure in millimeters of mercury inside a soap bubble 0.100 m in diameter?

$2\text{.}\text{23}×{\text{10}}^{-2}\phantom{\rule{0.25em}{0ex}}\text{mm Hg}$

Calculate the force on the slide wire in [link] if it is 3.50 cm long and the fluid is ethyl alcohol.

[link] (a) shows the effect of tube radius on the height to which capillary action can raise a fluid. (a) Calculate the height $h$ for water in a glass tube with a radius of 0.900 cm—a rather large tube like the one on the left. (b) What is the radius of the glass tube on the right if it raises water to 4.00 cm?

(a) $1\text{.}\text{65}×{\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}\text{m}$

(b) $3\text{.}\text{71}×{\text{10}}^{–4}\phantom{\rule{0.25em}{0ex}}\text{m}$

We stated in [link] that a xylem tube is of radius $2\text{.}\text{50}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\text{m}$ . Verify that such a tube raises sap less than a meter by finding $h$ for it, making the same assumptions that sap’s density is $\text{1050}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}$ , its contact angle is zero, and its surface tension is the same as that of water at $20.0º C$ .

What fluid is in the device shown in [link] if the force is $3\text{.}\text{16}×{\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}\text{N}$ and the length of the wire is 2.50 cm? Calculate the surface tension $\gamma$ and find a likely match from [link] .

$6\text{.}\text{32}×{\text{10}}^{-2}\phantom{\rule{0.25em}{0ex}}\text{N/m}$

Based on the values in table, the fluid is probably glycerin.

If the gauge pressure inside a rubber balloon with a 10.0-cm radius is 1.50 cm of water, what is the effective surface tension of the balloon?

Calculate the gauge pressures inside 2.00-cm-radius bubbles of water, alcohol, and soapy water. Which liquid forms the most stable bubbles, neglecting any effects of evaporation?

$\begin{array}{lll}{P}_{\text{w}}& =& \text{14}\text{.}6\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2},\\ {P}_{\text{a}}& =& \text{4.46}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2},\\ {P}_{\text{sw}}& =& \text{7.40}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}\text{.}\end{array}$

Alcohol forms the most stable bubble, since the absolute pressure inside is closest to atmospheric pressure.

Suppose water is raised by capillary action to a height of 5.00 cm in a glass tube. (a) To what height will it be raised in a paraffin tube of the same radius? (b) In a silver tube of the same radius?

Calculate the contact angle $\theta$ for olive oil if capillary action raises it to a height of 7.07 cm in a glass tube with a radius of 0.100 mm. Is this value consistent with that for most organic liquids?

$5.1º$

This is near the value of $\theta =0º$ for most organic liquids.

When two soap bubbles touch, the larger is inflated by the smaller until they form a single bubble. (a) What is the gauge pressure inside a soap bubble with a 1.50-cm radius? (b) Inside a 4.00-cm-radius soap bubble? (c) Inside the single bubble they form if no air is lost when they touch?

Calculate the ratio of the heights to which water and mercury are raised by capillary action in the same glass tube.

$-2\text{.}\text{78}$

The ratio is negative because water is raised whereas mercury is lowered.

What is the ratio of heights to which ethyl alcohol and water are raised by capillary action in the same glass tube?

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
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Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
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what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
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analytical skills graphene is prepared to kill any type viruses .
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
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How we can toraidal magnetic field
How we can create polaidal magnetic field
4
Because I'm writing a report and I would like to be really precise for the references
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!


text:
# obscure error in index file

I reduce my problem to the following example:

\documentclass{scrbook}
\usepackage[nochapters]{classicthesis}
\usepackage{tikz}
\usepackage{makeidx}

\makeindex

\begin{document}

\index{j}
\nocite{Salsa}

\begin{thebibliography}{1}
\bibitem{Salsa}
Salsa
\end{thebibliography}

\printindex

\end{document}

I compile the file with the command latexmk --pdf and get the following error:

! A <box> was supposed to be here.
\def
l.5 \end{theindex}

line numbers referring to the ind generated file which reads as:

\begin{theindex}

\item j, \hyperpage{1}

\end{theindex}

The error can be reproduced on the docker image: ghcr.io/xu-cheng/texlive-full

• Works for me when using pdflatex + makeindex + pdflatex (via arara).
– chsk
May 1, 2021 at 10:01
• The problem is the usual one: classicthesis loads hyperref at a wrong time. May 1, 2021 at 10:23


text:
# Finding internal resistance

1. Aug 8, 2010

### arkofnoah

1. The problem statement, all variables and given/known data
http://img408.imageshack.us/img408/6537/screenshot20100808at134.png [Broken]

2. Relevant equations

3. The attempt at a solution
I redrew the circuit as follow:

http://img293.imageshack.us/img293/6247/screenshot20100808at135.png [Broken]

Is this correct (or even useful in the first place)?

Anyway when switch S1 is closed, the total resistance = rx + ry, the internal resistances of the batteries.

But when both switches are closed, I figured that the voltage increased by 0.02V, to 0.07V. However I am not sure this is the voltage across which components because the millimeter is connected in a rather strange way.

I'm lost from here onwards. I'm mostly troubled by the placement of the millivoltmeter I guess.

Am I on the right track? Any alternative method?

The answer is (A) by the way.

Last edited by a moderator: May 4, 2017
2. Aug 8, 2010

### ehild

The ideal millivoltmeter has infinitely high resistance.

ehild

3. Aug 8, 2010

### arkofnoah

okay i was thinking about that. when switch 1 is closed there is no current, and when both switches are closed the entire circuit system is basically a series circuit because no current flows though the millivoltmeter.

but i don't know what is the implication of this :tongue: what does the 5.0mV mean? what does the change of 2.0mV mean? any clue?

4. Aug 8, 2010

### ehild

When S2 is open the branch wit R just does not exist. Draw this arrangement. It might help. The voltage of what does the voltmeter read?

ehild

5. Aug 8, 2010

### arkofnoah

alright. so 5.0mV would be the potential difference between the two cells. Since there is no current flowing this is equal to the emf difference between the two cells, correct? so i can effectively treat X and Y as if it is a single cell with emf 5.0mV, right?

when s2 is closed, will the voltage increase by 2.0mV or decrease by 2.0mV? i know there is now current flowing in the branch with S2 but can you elaborate how exactly does this affect the millivoltmeter reading?

6. Aug 8, 2010

### arkofnoah

Oh okay i think i get it. So initially the voltmeter reading of 5.0mV is

$$E_{x} - E_{y}$$ where Ex and Ey is the emf of X and Y.

Now after closing the circuit with R, current flows through the internal resistor of X and the voltmeter reading of 3.0mV is

$$V_{x} - E_{y}$$ where Vx is the terminal p.d. of X, which is lower than Ex its emf.

The difference of these two is basically

$$E_{x} - V_{x} = Ir$$ where r is the internal resistance of battery

So 2mV = 5.0(r) and r is 0.004 ohm.

Am I correct?

7. Aug 8, 2010

### ehild

Perfect, except two minor errors: The first voltage reading is 50 mV and the other one differs from this by 20 mV.

From 2 mv =r (5 A) --->r = 0.0004 ohm, but you get the correct result if you use the original 20 mV.

ehild

8. Aug 8, 2010

### arkofnoah

oh okay that's more of a typo :tongue:

thanks for your help!!