Question

Problem4: For á magnetic substance, thethermodynamie variables are the intensive magnetic fielH, and theextensive magnetization M,which are unidirectional and uniform in space. Since the work done by the magnetic system is given by dW-HdM we can compare it withdW PdV to determine the correspondence between the pairs of variables (H.M and (P.V). Write down the corresponding first law for a magnetic system where the number of particles is constant. Use your understanding of the ideal gas systems for the rest of the problem. If the heat capacity at constant H is denoted by Cu, and that at constant Mis CM. Show that

Answer 1

First law of thermodynamics for closed system, any general process, quasi- static or reversible is written as

$dU=TdS-PdV$

which is sometimes written as

$dU=dQ-dW$.

S is entropy.

Now for magnetic systems

$dW=-HdM$

so

$dU=TdS+HdM$