[QUE/TH-06006] TH-PROBLEM

Consider a paramagnetic system, with variables magnetization $M$, the magnetic field $B$ and absolute temperature $T$. ( We assume it's dependence on pressure as negligible). The equation of state is ( which will be obtained from statistical mechanics later in the course) is
$$ M\,=\,C\frac{B}{T}, $$
where $C$ is a constant ( referred to as the Curie constant, who had experimentally obtained this relation.
The system's internal energy is ( for a one-dimensional system)
$$ U\,=\,-MB.$$
The work done on the system by external surrounding is $-MdB$

(a) Write the expression for $DQ$ in terms of $dM$ and $dB$

(b) Write the equation for entropy change $dS$ in terms of $dM$ and $dB$

(c) Obtain the entropy $S$