Consider a perfect classical gas. Each gas particle has two single particle states, and 2 with energies & and 2. The gas is filled into a porous container, and the container is then put into a reservoir of the same type of particle and maintain at temperature T. The porous container can maintain the pressure inside the container, and the gas particles can move in and out of the container. Let N be the number of particles in the container. Derive the mean number of particles, N, variance of particles number, (AN), and entropy, S, of the gas.