• Support PF! Buy your school textbooks, materials and every day products Here!

Statistical physiics Problem 5.5

  • Thread starter ehrenfest
  • Start date
1,996
1
1. Homework Statement
http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/85482B93-6A5E-4E2F-ABD2-E34AC245396C/0/ps5.pdf [Broken]

I am stuck on Problem 5 part a. They say that the relevant state variables are H,M,T, and U. Obviously the first law of thermodynamics still holds: dU = dW+dQ (does anyone know how to make inexact differentials in latex)? But does dW = -PdV here? P and V were not among the state variables they talked about so does that really make sense? How do I proceed?


2. Homework Equations



3. The Attempt at a Solution
 
Last edited by a moderator:

Answers and Replies

1,996
1
anyone?
 
Mapes
Science Advisor
Homework Helper
Gold Member
2,592
17
[itex]dW=H\,dM[/itex] and [itex]U=TS+MH[/itex]. Work terms always consist of a generalized force (an intensive quantity) and a generalized displacement (an extensive quantity). Examples: force x distance, magnetic field x magnetization, electric field x polarization, surface energy x area, stress x strain, etc.

In this problem [itex]P\,dV[/itex] work is evidently assumed to be negligible compared to [itex]M\,dH[/itex] work. You can tell because the problem states that there are only two independent variables (recall our https://www.physicsforums.com/showthread.php?p=1645661#post1645661").
 
Last edited by a moderator:
1,996
1
OK, I see why [itex]dU = \delta Q +HdM[/itex]. But why is U = TS+MH true? I am trying to express [itex]C_M \equiv \left(\frac{\delta Q}{dT} \right)_M[/tex] as a derivative of the internal energy. Can you give me a hint how to do that?
 
Mapes
Science Advisor
Homework Helper
Gold Member
2,592
17
From what you've written, it looks like you can conclude that [itex]
C_M \equiv \left(\frac{\partial U}{\partial T} \right)_M
[/itex].

In general, [itex]
U=TS-PV+\sum\mu_i N_i +FL+ MH+EP+\gamma A+\sigma V\epsilon\dots
[/itex] where the terms represent the work terms I listed above. This is called the Euler form of the fundamental relation, if you want to find more information about it. Callen's Thermodynamics is a good reference.
 

Related Threads for: Statistical physiics Problem 5.5

  • Last Post
Replies
0
Views
911
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
221
  • Last Post
Replies
0
Views
787
  • Last Post
Replies
6
Views
4K
Replies
2
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Top