- #1

- 41

- 5

- Homework Statement:
- Since the problem is long, and my doubt is very specific, I'll show it in a picture, it is the problem 6. But summing up, the question is in the item ii) where it is asked to calculate the total thermal energy of the gas.

- Relevant Equations:
- U=nCvT ; PV=nRT;

We have that energy in a infinitesimal Spherical layer with number of mols dn is:

dU=Cv.T.dn (1)

But by the ideal gas law:

PV=nRT (2)

Differentiation gives:

PdV+VdP=RTdn (3)

(3) in (1) and using CV=3R/2 (monoatomic)

gives:

dU=3/2.(PdV+VdP) (4)

Integration of (4) over the whole gas will not give the result expected. Where is my mistake?