Obtain an expression of single particle partition function. Hence, using this expression obtain expressions for entropy and pressure.

The single particle partition function, denoted by \( q_1 \), represents the contribution of a single particle to the overall partition function of a system in thermal equilibrium. It is defined as the sum of the Boltzmann factors over all the possible energy states \( E_i \) of the particle:

\[ q_1 = \sum_{i} e^{-\beta E_i} \]

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