Maxwell relation with 3 variables?

Click For Summary
SUMMARY

The discussion centers on deriving a Maxwell relation involving three variables: entropy (S), temperature (T), volume (V), pressure (P), magnetization (M), and magnetic field (B). The user starts with the thermodynamic potential dG = -SdT + VdP - MdB and successfully identifies the relationships (dG/dB)_(T,P) = -M and (dG/dT)_(P,B) = -S. The user initially struggles with the application of partial differentials but ultimately resolves their confusion by consulting a thermodynamics textbook.

PREREQUISITES
  • Understanding of thermodynamic potentials, specifically Gibbs free energy (dG).
  • Familiarity with partial differentiation in thermodynamics.
  • Knowledge of Maxwell relations and their significance in thermodynamics.
  • Basic concepts of magnetization (M) and magnetic field (B) in thermodynamic contexts.
NEXT STEPS
  • Study the derivation and implications of Maxwell relations in thermodynamics.
  • Explore the role of magnetic fields in thermodynamic systems, focusing on magnetization (M).
  • Review the properties and applications of Gibbs free energy in phase transitions.
  • Investigate the relationship between entropy (S) and temperature (T) in various thermodynamic processes.
USEFUL FOR

Students and professionals in physics and engineering, particularly those specializing in thermodynamics, magnetism, and related fields.

anony
Messages
13
Reaction score
0
Hello,
I have the thermodynamic potential dG = -SdT + VdP - MdB and I find that

(dG/dB)_(T,P) = -M and (dG/dT)_(P,B) = -S, where I have used _(letters) to denote constants and that these are partial differentials. I want to prove the Maxwell relation that

(dS/dB)_(T,P) = (dM/dT)_(B,P) *

so I do

(d/dB (dG/dT)_(P,B))_(T,P) = (d/dT (dG/dB)_(T,P))_(P,B)

But then bring these partials together, I no longer no what it supposed to be kept constant, or how I get to *

Sorry, about the messiness, and cheers for any help. I didn't put this in the homework section because its a pretty general question rather that an actual problem.

EDIT: Nevermind, I'm being an idiot. I got it now.
 
Last edited:
Physics news on Phys.org
' Have found my thermodynamics book and see that I understand What S,T,V and P are.
What are M and B here?
 

Similar threads

Graduate Maxwell Relations: when are they valid?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Gibbs Free Energy Correction Term
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Maxwell's Equations, Dielectrics, Auxiliary Fields D and H
  • · Replies 16 ·
Replies
16
Views
3K
Chemistry How to derive 2nd law extremum principles for U, A, G, and H?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Frequency in Maxwell's equations
  • · Replies 19 ·
Replies
19
Views
3K
Undergrad Minimization of the Gibbs energy when number of molecules varies
  • · Replies 16 ·
Replies
16
Views
3K
Graduate Confusion when dealing with loops and surfaces with Maxwell equations
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Dirac's derivation of the action/Lagrangian for a free particle
  • · Replies 3 ·
Replies
3
Views
1K
DeltaG and DeltaA calculation for heating a gas at constant volume
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Electric and magnetic field lines in a plane wave of finite extent
  • · Replies 1 ·
Replies
1
Views
2K