Maxwell's relation Thermodynamics

hasibme2k
How can I prove the following relation
T(∂p/∂T)v,N +(∂T/∂V)u,N =p(∂T/∂U)v,N

where p= pressure, V= volume, U=internal energy, T= Temperature. I tried by fundamental relation and Maxwell's relation but couldn't able to prove it.

I would appreciate if anybody helps me out.

Last edited:

Answers and Replies

Science Advisor
Gold Member
Are those partial derivatives? If so use "advanced" so we can be sure. Is t the same as T?

Science Advisor
Gold Member
2021 Award
...and you also need to tell which variables are kept constant when taking the partial derivatives like in, e.g.,
$$C_V=\left (\frac{\partial U}{\partial T} \right )_{V,N}$$
to define the specific heat at constant volume.

Science Advisor
Homework Helper
That's the trick with thermodynamics. Partial derivatives always come from maths with something extra: which variables specifically you are keeping constant when calculating the limits of a multivariable function.

Gold Member
I think the relationship is wrong. The dimensions of the first term are those of pressure, but the dimensions of the other two terms are those of temperature divided by volume.