The partition function for a gas is given by

Q(N, V, T) =  (v - Nb)N 

The internal energy of the gas is

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Concept:

  • The Maxwell–Boltzmann distribution concerns the distribution of an amount of energy between identical but distinguishable particles.
  • It represents the probability for the distribution of the states in a system having different energies. A special case is the so-called Maxwell distribution law of molecular velocities.
  • The final expression for the internal energy U of a system following the Boltzmann distribution of energy is:

 

U = .......(1)

Explanation:-

  • The partition function for a gas is given by

Q(N, V, T) =  (v - Nb)N.........(2)

  • By taking ln both the sides of equation (2) we got,

or, 

or, 

or, 

or, 

or,

  • Now, putting the value of  in equation (1) we get,

or, U = kBT2 ×  -  kBT2 × 

or, U = 

Conclusion:-

Hence, the internal energy of the gas is 

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