# A A technical question about the Joule-Thomson Experiment

1. Nov 20, 2017

### MathematicalPhysicist

It's written in Kubo's textbook:

I tried getting (2) from (1), but I get something different, I get:
$T\partial V / \partial T - V = TR/p+TRB+RT^2dB/dT-RT/p-RTB = RT^2dB/dT$, how to resolve this conundrum?

Thanks.

2. Nov 20, 2017

### DoItForYourself

Hi,

It seems that you must prove $RT=1-\frac {B} {T\frac{dB} {dT}}$.

3. Nov 20, 2017

### MathematicalPhysicist

Seems so.

4. Nov 20, 2017

### DoItForYourself

The equation pV=RT(1+Bp) is false.

The general equation is $pV=RT+B(T)p+C(T)p^2+D(T)p^3+.$.
If you consider C,D,...=0, then you can end up to the following equation:
$\left( \frac {\partial T} {\partial p} \right)_H=\frac {\left( T\left( \frac {\partial V} {\partial T} \right)_p-V \right)} {C_p}=\frac {\left( T \frac {\partial \left(\frac {RT+Bp} {p} \right)_p} {\partial T}-\frac {RT+Bp} {p} \right)} {C_p} \Rightarrow$
$\left( \frac {\partial T} {\partial p} \right)_H = \frac { \left( \frac {RT} {p} +T \frac {dB} {dT} - \frac {RT}{p} - B\right)} {C_p}=\frac {T \frac {dB} {dT}-B} {C_p}$

Last edited by a moderator: Nov 20, 2017
5. Nov 20, 2017

### MathematicalPhysicist

How do you get the last identity from $pV = RT+B(T)p$?, I don't see it.

6. Nov 20, 2017

### DoItForYourself

I edited the post, so you can see the detailed process that I followed to reach the final result.

7. Nov 20, 2017