Consider a system in thermal equilibrium, having energies 0 and 'E'. Find the partition function (Z) and Entropy (S) of the system.

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Consider a system in thermal equilibrium, having energies 0 and &#039;E&#039;. Find the partition function (Z) and Entropy (S) of the system.

percolarse2rzd · Accepted Answer

The partition function (Z) can be written as below,  Z  =      ∑          i      =      1        2        g    i        e          −              β        i                    ϵ        i              =      ∑          i      =      1        2        e          −              β        i                    ϵ        i                =      e          −      β              ϵ        1              +      e          −      β              ϵ        2                =      e          −      β      (      0      )        +      e          −      β      E          =  1  +      e          −      β      E      Here   β  =  1      /        k    B    T, where       k    B   is the Boltzmann’s constant and T is the absolute temperature.The entropy of the system can be calculated, after substituting the above obtained expression as below,  S  =  (  −            d      F              d      T            )    V      =  −      d          d      T        [  −      k    B    T  ln  ⁡  (  1  +      e          −      E              /                    k        B            T        )  ]    =      k    B        d          d      T        [  T  ln  ⁡  (  1  +      e          −      E              /                    k        B            T        )  ]    =      k    B    ln  ⁡  (  1  +      e          −      E              /                    k        B            T        )  +            e              −        E                  /                          k          B                T                    1      +              e                  −          E                      /                                k            B                    T                    This is the required entropy of the system.

Consider a system in thermal equilibrium, having energies 0 and

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