Determine the grand partition function of a gaseous system of "magnetic" atoms (with \(J=\frac{1}{2}\) and \(g=2\) ) that can have, in addition to the kinetic energy, a magnetic potential energy equal to \(\mu_{B} H\) or \(-\mu_{B} H\), depending on their orientation with respect to an applied magnetic field \(H\). Derive an expression for the magnetization of the system, and calculate how much heat will be given off by the system when the magnetic field is reduced from \(H\) to zero at constant volume and constant temperature.