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4. a) A classical system consists of N particles and have a total energy of E. The particles are distributed in different energy states i such that $N = \sum_i N_i$ and $E = \sum_i E_i$ where $N_i$ and $E_i$ are the number of particles and the energy of the state i, respectively. Calculate the thermodynamic probability \Omega and obtain the equilibrium distribution of {$N_i$} by maximizing the entropy S of the system with respect to the occupation number $N_i$. b) Comment on how the equilibrium distribution of the particles in 4(a) would be affected if the total energy of the system is not conserved but an average energy can be defined. What is the physical significance of this observation?

          4. a) A classical system consists of N particles and have a total energy of E. The particles are distributed in different energy states i such that
$N = \sum_i N_i$ and $E = \sum_i E_i$
where $N_i$ and $E_i$ are the number of particles and the energy of the state i, respectively. Calculate the thermodynamic probability \Omega and obtain the equilibrium distribution of {$N_i$} by maximizing the entropy S of the system with respect to the occupation number $N_i$.
b) Comment on how the equilibrium distribution of the particles in 4(a) would be affected if the total energy of the system is not conserved but an average energy can be defined. What is the physical significance of this observation?

4. a) A classical system consists of N particles and have a total energy of E. The particles are distributed in different energy states i such that
N = Ni and E = Ei
where Ni and Ei are the number of particles and the energy of the state i, respectively. Calculate the thermodynamic probability Ωand obtain the equilibrium distribution of Ni by maximizing the entropy S of the system with respect to the occupation number Ni.
b) Comment on how the equilibrium distribution of the particles in 4(a) would be affected if the total energy of the system is not conserved but an average energy can be defined. What is the physical significance of this observation?

Added by James N.

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