(20) 4. Density of States for an Ideal Gas: Application of Microcanonical Formalism In class we used a quantum mechanical treatment to solve for the energies of N non-interacting particles of mass m in a cubic box with sides L and proceeded to determine the density of states D(E) for the gas. It was related to the number of states within the energy range (E,E)= D(E)E. Using the expression derived in class D(E)=N!VN(h22m)3N/2(23N+1)E3N/21 i) give an expression for the entropy S for a given energy, volume, and particle number, and ii) neglecting the term log(E/E) obtain an expression for the temperature using the appropriate thermodynamic definition. It should agree with the well-known equation of state for a monatomic ideal gas E=23NkBT. Why can you neglect the above term? iii) And finally using another thermodynamic definition from the entropy representation for the pressure, derive the well-known equation of state for the ideal gas