Are Thermodynamic Equations Considered PDEs?

Click For Summary

Discussion Overview

The discussion centers around the classification of thermodynamic equations, specifically whether they should be considered partial differential equations (PDEs) due to their use of partial derivatives. Participants explore the nature of these equations in the context of thermodynamics and their mathematical implications.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant notes that thermodynamic equations involve partial derivatives but questions whether they should be classified as PDEs, as they are not referred to as such in their textbook.
  • Another participant argues that these are not equations but equalities, emphasizing the absence of unknown functions and boundary conditions, and suggests that one must determine the form of the functions involved before differentiating.
  • A later reply acknowledges the clarification that these relations do not need to be solved, reinforcing the idea that they merely express relationships between thermodynamic functions.

Areas of Agreement / Disagreement

Participants generally agree that thermodynamic equations are not equations in the traditional sense requiring solutions, but there is some contention regarding their classification as PDEs.

Contextual Notes

The discussion does not resolve the classification of thermodynamic equations as PDEs, and it remains unclear how the definitions of equations and equalities apply in this context.

MexChemE
Messages
237
Reaction score
54
Hello, PF! As I was reading my P-Chem textbook, I noticed most thermodynamic equations involve partial derivatives, like these ones: C_V = {\left( \frac {\partial E}{\partial T} \right )}_V {\left( \frac {\partial H}{\partial T} \right )}_P = {\left( \frac {\partial E}{\partial T} \right )}_P + P{\left( \frac {\partial V}{\partial T} \right )}_P However, none of these equations is ever actually called a PDE by the author. Is it implied they are PDEs given they involve partial derivatives, or are they not classified as PDEs such as the wave or heat equations? Thanks in advance!
 
Last edited:
Physics news on Phys.org
They are not equations, but equalities, because there's no unknown function and no boundary conditions. In the first equality you wrote, you should determine what E(T,V) looks like, then partially differentiate wrt T, to get the function C_V(T,V). For the second, there's an equality involving 3 different functions, H(T,P), E(T,P) and V(T,P).
 
I get it now, they are not equations in the sense that they need not be solved, right? They are just showing the relation between thermodynamic functions.
 
MexChemE said:
I get it now, they are not equations in the sense that they need not be solved, right? They are just showing the relation between thermodynamic functions.
Right.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 36 ·
2
Replies
36
Views
6K