1. Consider an isolated classical ideal gas with N molecules in a 3 - D box of volume V. Calculate the equilibrium properties of this system using the formalism of a micro- canonical ensemble following the steps as enumerated below: (a) Write down the Hamiltonian H for the system. [1] (b) Compute the expression for (E, V, N), the phase-space volume corresponding to the total energy lying between E and E+ A, i.e, E < H < E + A. [3] (c) Compute the expression for entropy S(E,V,N). [2] (d) Calculate the expression for E(T, V, N). (e) Calculate the equation of state of the system. [2] [2]