# Van der Waals Gas

1. Jan 30, 2016

### krootox217

1. The problem statement, all variables and given/known data
Hi, I have the following task:

Translated into English, that means:

" For Cpm and Cvm of gases the following relationship is true: (1)
a) Show with the relationship (1), that for an ideal gas Cpm - Cvm = R is valid
b) Deduce from equation (1) and the tripple product rule Cpm - Cvm for a Van der Waals gas (dependent on Vm, T and also R, a and b)"

I managed to solve a) but I don't know how to solve b)
Can someone help me?

2. Relevant equations
Tripple product rule: https://en.wikipedia.org/wiki/Triple_product_rule
Van der Waals equation: https://de.wikipedia.org/wiki/Van-der-Waals-Gleichung

3. The attempt at a solution
see above

2. Jan 30, 2016

### Staff: Mentor

Chet

3. Jan 30, 2016

### krootox217

For a) I used p*Vm=RT

then I solved the equation once for p and once for Vm, and did the partial derivatives, which yielded T*(R/p)*(R/Vm) = Cpm- Cvm = (T*R2)/(p*Vm)

and then I said p*Vm=R*T and i reduced the fraction, which yielded Cpm- Cvm = R

But I don't understand how to start in the second task, could you help me?

4. Jan 30, 2016

### Staff: Mentor

I would start out by evaluating each of the partial derivatives in Eqn. 1 and see what I get. If that doesn't give me what I'm looking for, I would start thinking about ways in which the triple product rule might get me to where I want to be. Maybe you're going to have to "play with the math" at little.

Chet

5. Jan 30, 2016

### krootox217

Did I understand you correctly that I should do the same as in a), but this time not with the ideal gas equation, but with the van der waals equation?

6. Jan 30, 2016

### Staff: Mentor

Sure. The problem statement indicates that the final answer should include all the parameters except for P. To me, this means that the first partial derivative in Eqn. 1 might be troublesome. See how it all plays out. Start by evaluating the two partial derivatives in equation 1 based on the van der waals equation.

7. Jan 30, 2016

### krootox217

Ok, thanks a lot! :)