# Homework Help: Heat Transfer Between Reservoirs due to Magnetic Fields

1. Jul 5, 2008

### SonOfOle

1. The problem statement, all variables and given/known data
A system consists of N pairs of non-interacting, spin 1/2 particles with magnetic moment $$\mu$$. It is initially immersed in a uniform magnetic field $$H_{i}$$ while it is in thermal equilibrium with a reservoir at temperature $$T_{i}$$. While remaining in thermal equilibrium with the reservoir, the magnetic field increased to a value of $$H_{f}$$. At this point the system is isolated from the reservoir and the magnetic field returns adiabatically to $$H_{i}$$. The system is then brought into thermal equilibrium with a second reservoir at temperature $$T_{f}$$.

(A) How much work is done on the system by the magnetic field?

(B) How much heat is transferred between the two reservoirs?

2. Relevant equations
$$U_{total}=N \mu H$$
$$\delta U = Q + W$$

3. The attempt at a solution

(A) Magnetic fields can't do work, so $$W=0$$.
(B) Recall relevant equations, so $$N \mu H = Q$$.

This seems like it, but I don't think it is. The temperature doesn't play a role. Does it mean the additional heat transferred to the solution in (B) is the change in energy due to temperature (e.g. $$\delta U = n R \delta T$$?

2. Jul 5, 2008

### Astronuc

Staff Emeritus
Is one sure about that. If magnetic field flips a magnetic dipole or attracts a metal (e.g. ferromagnetic) object, what is doing the work?

Are all the magnetic moments aligned initially?

How does the magnitudes of the applied magnetic fields compare with the field strength of the magnetic dipole?

3. Jul 8, 2008

### SonOfOle

Hey Astronuc, thanks for the reply. To honestly reply to your questions, I'm not sure. This is a problem I ran into as I'm reviewing past qualification exams in preparation for my upcoming one in August.

My E&M class was weak in the "M", and so I'm wondering if you--or anyone--could point me in the right direction. I've got Griffiths Intro to Electrodynamics, so even referring to places in there to read would help.