Stuck on Understanding Work Terms in Statistical Physics Problem 5.5?

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Homework Help Overview

The discussion revolves around understanding the work terms in a statistical physics problem, specifically Problem 5 part a from a course assignment. The relevant state variables mentioned include enthalpy (H), magnetization (M), temperature (T), and internal energy (U). The original poster expresses confusion regarding the application of the first law of thermodynamics and the role of pressure (P) and volume (V) in this context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between work terms and state variables, questioning the relevance of P and V in the absence of explicit mention. There is an attempt to clarify the expression for internal energy and its relation to heat capacity.

Discussion Status

Some participants have provided insights into the formulation of work terms and the assumptions made regarding negligible P\,dV work compared to M\,dH work. There is ongoing exploration of how to express heat capacity in terms of internal energy, indicating a productive direction in the discussion.

Contextual Notes

The original poster seeks clarification on the use of inexact differentials in LaTeX and expresses uncertainty about the definitions and relationships of the state variables involved in the problem.

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Homework Statement


http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/85482B93-6A5E-4E2F-ABD2-E34AC245396C/0/ps5.pdf

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?


Homework Equations





The Attempt at a Solution

 
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anyone?
 
[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").
 
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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?[/itex]
 
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.
 

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