1. Consider an isolated classical ideal gas with N molecules in a 3 - D box...

 

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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] 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]

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first we will analyze the ideal gas using the microcanonical ensemble approach a HamiltonianH For a classical ideal gas the total energy arises solely ... View the full answer