PS4 5b

In the PS4 5b, showing dCp/dV=0, some used

d/dV [ (dS/dT)_P ]_T = d/dT[ (dS/dV)_T]_P,

However, this converstion does not give 0.

You can't switch the order of the derivatives because they are not compatible (you have different independent variables). d/dV [ (dS/dT)_P ]_T not equal to d/dT[ (dS/dV)_T]_P

To do the switch, you have to have the same set of independent variables. You could do this, for example:

d/dV [(dS/dT)_P]_T
= (dP/dV)_T * d/dP[(dS/dT)_P]_T
= (dP/dV)_T * d/dT[(dS/dP)_T]_P

And then you will find that the right hand term is zero.

Hope that helps,
Scott