Is This Thermodynamic Relationship Correct?

Click For Summary

Homework Help Overview

The discussion revolves around a thermodynamic relationship involving pressure, volume, internal energy, and temperature. The original poster attempts to prove a specific equation involving partial derivatives but expresses difficulty in doing so using fundamental and Maxwell's relations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants question the notation and clarity of the variables involved, particularly regarding the use of partial derivatives and the constants held during differentiation. There are discussions about the dimensional consistency of the terms in the equation.

Discussion Status

The conversation is ongoing, with participants raising clarifying questions and expressing differing opinions on the validity of the relationship. Some guidance on the importance of specifying constant variables during differentiation has been provided, but no consensus has been reached regarding the correctness of the relationship.

Contextual Notes

There is an emphasis on the need for clarity in notation and the definitions of the variables involved, as well as the importance of understanding the implications of keeping certain variables constant in thermodynamic equations.

hasibme2k
Messages
2
Reaction score
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:
Physics news on Phys.org
Are those partial derivatives? If so use "advanced" so we can be sure. Is t the same as T?
 
...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.
 
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.
 
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.
 

Similar threads

Replies
7
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
30
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
5K
  • · Replies 26 ·
Replies
26
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
1
Views
4K
Replies
4
Views
1K