Maxwell's relation Thermodynamics

  • Thread starter hasibme2k
  • Start date
  • #1
hasibme2k
3
0
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

  • #2
UltrafastPED
Science Advisor
Gold Member
1,914
216
Are those partial derivatives? If so use "advanced" so we can be sure. Is t the same as T?
 
  • #3
vanhees71
Science Advisor
Insights Author
Gold Member
2021 Award
21,132
12,016
...and you also need to tell which variables are kept constant when taking the partial derivatives like in, e.g.,
[tex]C_V=\left (\frac{\partial U}{\partial T} \right )_{V,N}[/tex]
to define the specific heat at constant volume.
 
  • #4
dextercioby
Science Advisor
Homework Helper
Insights Author
13,239
999
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.
 
  • #5
Philip Wood
Gold Member
1,221
78
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.
 

Suggested for: Maxwell's relation Thermodynamics

Replies
4
Views
190
Replies
8
Views
829
  • Last Post
Replies
2
Views
5K
Replies
11
Views
792
Replies
3
Views
1K
Replies
1
Views
346
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
10
Views
1K
Top