Consider a system of non-interacting spins in an applied magnetic field $H$. Using $S=k(\ln Z+\beta E)$, where $Z$ is the partition function, $E$ is the energy, and $\beta=1 / k T$, argue that the dependence of $S$ on $H$ and $T$ is of the form $S=f(H / T)$ where $f(x)$ is some function that need not be determined.
Show that if such a system is magnetized at constant $T$, then thermally isolated, and then demagnetized adiabatically, cooling will result.
Why is this technique of adiabatic demagnetization used for refrigeration only at very low temperatures?
How can we have $T<0$ for this system? Can this give a means of achieving $T=0$ ?