can you please post solutions to problems 1,2,4 and 10 fr Ch 6?

poynting 1238659431|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 6 / Solutions » can you please post solutions to problems 1,2,4 and 10 fr Ch 6?

please do! thanks a lot!

can you please post solutions to problems 1,2,4 and 10 fr Ch 6? by

poynting, 1238659431|%e %b %Y, %H:%M %Z|agohover

can anyone please post solutions to questions 3,7,13, and 14 in Ch 5?

poynting 1238659342|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 5 / Solutions » can anyone please post solutions to questions 3,7,13, and 14 in Ch 5?

please! thank you! i badly need them.

can anyone please post solutions to questions 3,7,13, and 14 in Ch 5? by

poynting, 1238659342|%e %b %Y, %H:%M %Z|agohover

Re: Welcome

bocho1986 1237418238|%e %b %Y, %H:%M %Z|agohover
in discussion General Forum / Discussion » Welcome

Hello,

I will start to solve several problems on this book starting this coming week. I will like to help by posting the solutions. Can you provide the password so I can post solutions? email me at ude.csu|orravanf#ude.csu|orravanf.

Thanks,

Francisco

Re: Welcome by

bocho1986, 1237418238|%e %b %Y, %H:%M %Z|agohover

sorry doubt above problems in "fundamentals of statistical and thermal physics" of F.Reif

sursum 1235446845|%e %b %Y, %H:%M %Z|agohover
in discussion General Forum / Discussion » sorry doubt above problems in "fundamentals of statistical and thermal physics" of F.Reif

in problems 1.4, 1.7 and 1.9!!!

thnxs!!!!

sorry doubt above problems in "fundamentals of statistical and thermal physics" of F.Reif by

sursum, 1235446845|%e %b %Y, %H:%M %Z|agohover

Problem 7

smnhasan 1225332404|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 12 / Solutions » Problem 12-7

Can any one please solve it for me?

Problem 7 by

smnhasan, 1225332404|%e %b %Y, %H:%M %Z|agohover

Solution: Problem1-46

siroma 1222692955|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 1 / Solutions » Solution: Problem1-46

(1)

$W(X,Y)=X+Y$

Expected value of W:

(2)

$\begin{tabular}{ccl} E(W) & \stackrel{\text{by def.}}{=} & \iint{(x+y)f(x,y)dxdy \ & = & \iint{xf(x,y)dxdy} + \iint{yf(x,y)dxdy \ & \stackrel{\text{indep.} }{=} & \iint{xf_1(x)f_2(y)dxdy + \iint{yf_1(x)f_2(y)dxdy\ & = &\int{xf_1(x)dx}\int{f_2(y)dy} + \int{yf_2(y)dy}\int{f_1(x)dx}\ & = &\int{xf_1(x)dx} + \int{yf_2(y)dy}\ & = & E(X)+ E(Y) \end{tabular}$

Variance of W:

(3)

$\begin{tabular}{ccl} Var(W) & \stackrel{\text{by def.}}{=} & \iint{((x+y)-E(X+Y)})^2}f(x,y)dxdy \ & = & \iint{((x-E(X))+(y-E(Y)))^2f(x,y)dxdy} \ & = & \iint{(x-E(X))^2f(x,y)dxdy + \\ & & 2\iint{(x-E(X))(y-E(Y))}f(x,y)dxdy + \ & & \iint{(y-E(Y))f(x,y)dxdy\ & \stackrel{\text{indep.} }{=} & \int{(x-E(X))^2f_1(x)dx\int{f_2(y)dy} +\ & & 2\int{(x-E(x))f_1(x)dx}\int{(y-E(y))f_2(y)dy}+\\ & & \int{(y-E(Y))^2f_2(y)dy\int{f_1(x)dx}\ & = & Var(X) + Var(Y) \end{tabular}$

Solution: Problem1-46 by

siroma, 1222692955|%e %b %Y, %H:%M %Z|agohover

Solution: Problem1-57

siroma 1222339519|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 1 / Solutions » Solution: Problem1-57

Geometric progression sum formula derivation:

(1)

$S_n=\sum_{n=0}^\infty {q^{n}a_0}=a_0+qa_0+q^2a_0+...+q^na_0$

(2)

$qS_n=q\sum_{n=0}^\infty {q^na_0}=qa_0+q^2a_0+q^3a_0+...+q^{n+1}a_0$

(3)

$(q-1)S_n=q^{n+1}a_0-a_0$

(4)

$S_n=a_0\frac{q^{n+1}-1}{q-1}$

If q<1 then

(5)

$\lim_{n \to \infty } S_n = a_0\frac{1}{1-q}$

In the problem $a_0=1$ and $q=e^{-\alpha}$ therefore we require that $e^{-\alpha} < 1$ ; thus when $\alpha>0$ we have closed sum

(6)

$\lim_{n \to \infty } S_n = \frac{1}{1-e^{-\alpha}}$

On the other hand,

(7)

$I=\int_{0}^{\infty}{e^{-\alpha n}}dn = -\frac{e^{-\alpha n}}{\alpha} |_0^\infty = -\frac{1}{\alpha}(\lim_{n \to \infty} e^{-\alpha n} - 1)$

Because $\alpha>0$

(8)

$I = \frac{1}{\alpha}$

To find required $\alpha$ we have

(9)

$\frac{1}{\alpha}=\frac{1}{1-e^{-\alpha}}$

or

(10)

$e^{-\alpha}=1-\alpha$

Equation (10) has only one solution(this can be shown comparing derivatives of rhs and lhs functions):

(11)

$\alpha=0$

To satisfy requirement of $\alpha > 0$ we give result in limit form:

(12)

$I \to S \text{ when } \alpha \to 0^+$

Solution: Problem1-57 by

siroma, 1222339519|%e %b %Y, %H:%M %Z|agohover

Solution: Problem1-55

siroma 1222308579|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 1 / Solutions » Solution: Problem1-55

Even function: f(x)=f(-x)

(1)

$f(-x)=\frac{e^{-x}}{(1 \pm e^{-x})^2}=\frac{e^{-x}}{(1\pm\frac{1}{e^x})^2}=\frac{e^{-x}e^{2x}}{(e^x\pm1)^2}=\frac{e^x}{(1 \pm e^x)^2}=f(x)$

QED

Solution: Problem1-55 by

siroma, 1222308579|%e %b %Y, %H:%M %Z|agohover

Solution: Problem1-30

siroma 1222306078|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 1 / Solutions » Solution: Problem1-30

Part 1

1st law:

(1)

$du=\delta{Q}+\delta{W}=Tds-Pdv$

Enthalpy definition:

(2)

$h=u+Pv$

Enthalpy differential:

(3)

$dh=du+Pdv+vdP=Tds+vdP$

Maxwell equation from (2):

(4)

$(\frac{\partial{T}}{\partial{P}})_v=(\frac{\partial{v}}{\partial{s}})_T$

Definition of heat capacity and insertion (1) into definition:

(5)

$c_v=(\frac{\partial{u}}{\partial{T}})_v=T(\frac{\partial{s}}{\partial{T}})_v$

Write entropy as function of T and v:

(6)

$s=s(T,v)$

Derive expression for entropy differential and use (4) and (5):

(7)

$ds=(\frac{\partial{s}}{\partial{T}})_vdT+(\frac{\partial{s}}{\partial{v}})_T=\frac{c_v}{T}dT+(\frac{\partial{P}}{\partial{T}})_vdv$

Insert (7) into (1):

(8)

$du=\delta{Q}+\delta{W}=Tds-Pdv=T(\frac{c_v}{T}dT+(\frac{\partial{P}}{\partial{T}})_vdv)-Pdv=(T(\frac{\partial{P}}{\partial{T}})_v -P)+c_vdT$

QED

Part 2

van der Waals equation:

(9)

$(p+\frac{a}{v^2})(v-b)=kT$

Express p:

(10)

$p=\frac{kT}{v-b}-\frac{a}{v^2}$

At constant T equation (8) becomes:

(11)

$(\frac{\partial{u}}{\partial{v}})_T=T(\frac{\partial{P}}{\partial{T}})_v-p$

Differentiate (10) at constant v and put into (11):

(12)

$T(\frac{\partial{P}}{\partial{T}})_v-p=\frac{kT}{v-b}-p=\frac{a}{v^2}$

QED

Solution: Problem1-30 by

siroma, 1222306078|%e %b %Y, %H:%M %Z|agohover

Re: including pdf documents

juliantalbot 1221818895|%e %b %Y, %H:%M %Z|agohover
in discussion General Forum / Discussion » including pdf documents

Re: including pdf documents by

juliantalbot, 1221818895|%e %b %Y, %H:%M %Z|agohover

including pdf documents

juliantalbot 1221818281|%e %b %Y, %H:%M %Z|agohover
in discussion General Forum / Discussion » including pdf documents

pdf documents can be incorporated in posts.

including pdf documents by

juliantalbot, 1221818281|%e %b %Y, %H:%M %Z|agohover

solution

deepali 1204398487|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 1 / Solutions » solution

can somebody post 1-51

solution by

deepali, 1204398487|%e %b %Y, %H:%M %Z|agohover

Re: Chapter 2 Questions

deepali 1204398392|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 2 / Solutions » Chapter 2 Questions

can somebody post 2-2,2-6,2-11

Re: Chapter 2 Questions by

deepali, 1204398392|%e %b %Y, %H:%M %Z|agohover

Re: McQuarrie 1-24

subbareddy 1196876116|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 1 / Solutions » McQuarrie 1-15

Does any one have solution for this?

Re: McQuarrie 1-24 by

subbareddy, 1196876116|%e %b %Y, %H:%M %Z|agohover

Problem 10,19,20

doufas 1196030824|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 4 / Solutions » Problem 10,19,20

Does anybody have thoughts on #s 10, 19, or 20?

Problem 10,19,20 by

doufas, 1196030824|%e %b %Y, %H:%M %Z|agohover

Re: posting solutions

fizzixmom 1194977349|%e %b %Y, %H:%M %Z|agohover
in discussion General Forum / Discussion » posting solutions

Click on the

(1)

$\surd x$

(the "mathematical equation" button), then use LaTeX to type your equations.

If you are new to LaTeX, you can learn it quickly at [http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/]

Re: posting solutions by

fizzixmom, 1194977349|%e %b %Y, %H:%M %Z|agohover

Re: Chapter 2 Questions

fizzixmom 1194976051|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 2 / Solutions » Chapter 2 Questions

I already turned my solutions in, but will try to post as soon as I get them back.

Re: Chapter 2 Questions by

fizzixmom, 1194976051|%e %b %Y, %H:%M %Z|agohover

testing

fizzixmom 1194975936|%e %b %Y, %H:%M %Z|agohover
in discussion General Forum / Discussion » testing

I'm new to wikidot, and trying to figure out if I need to be a member to post a message. I guess we'll see if this works.

testing by

fizzixmom, 1194975936|%e %b %Y, %H:%M %Z|agohover

Chapter 2 Questions

doufas 1194818707|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 2 / Solutions » Chapter 2 Questions

Does anybody know #2-2, 2-12 or 2-14?

Chapter 2 Questions by

doufas, 1194818707|%e %b %Y, %H:%M %Z|agohover

can anyone help me for the solution5.7

kal-el 1193677762|%e %b %Y, %H:%M %Z|agohover
in discussion Chapter 5 / Solutions » can anyone help me for the solution5.7

does anybody knowthe solution for 5.7?

can anyone help me for the solution5.7 by

kal-el, 1193677762|%e %b %Y, %H:%M %Z|agohover

Statistical Mechanics

Expected value of W:

Variance of W:

Part 1

Part 2

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