How Do You Calculate the Molar Entropy of a Gas?

leviathanX777 · Apr 21, 2010

Homework Statement

Show that the molar entropy of a gas is given by;

$5Cfrac%7B5%7D%7B2%7D%20%2B%20%20%5Cfrac%7B3%7D%7B2%7Dln%5Cfrac%7B2%5Cpi%20mk%7D%7Bh%5E2%7D%20%5D.jpg$

$latex2png.2.php?z=100&eq=S%20%3D%20(%5Cfrac%7B%5Cpartial%20F%7D%7B%5Cpartial%20T%7D)_v.jpg$

I've tried this numerous times. The first part of the question involved getting ln Z for the hemholtz free energy which was found to be;

$&eq=ln%5B%5Cfrac%7BeV%7D%7BN%7D(%5Cfrac%7B2%5Cpi%20mkt%7D%7Bh%5E2%7D)%5E%5Cfrac%7B3%7D%7B2%7D%5D.jpg$

The 3/2 is a power. I have tried this numerous times and still unable to get the result mentioned.

Mapes · Apr 21, 2010

Can you show your steps? It's just a matter of differentiating F and playing with a few terms. Also, [itex]S=-(\partial F/\partial T)_V[/itex].