When $\mathrm{T} \rightarrow \infty$, value of the single-particle partition function will be (given : degeneracy of level $j=g_{j}$ ) :
(a)1
(b)$\mathrm{g}_{0}$
(c)$\sum_{j}g_{j}$
(d)$1/\sum_{j}g_{j}$
Answer
SELF-PRACTICE — the source book printed no answer.
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Explanation
Partition function is given by $q=\sum_{j} g e^{\frac{-\epsilon_{g}}{kT}}$$Q=g_{0}+g_{1}e^{\frac{-\epsilon_{1}}{kT}}+g_{2}e^{\frac{-\epsilon_{2}}{kT}}+\ldots\ldots g_{j}e^{\frac{-\epsilon_{j}}{kT}}$$q=g_{1}+g_{2}+g_{3}+\ldots\ldots g_{j}$$q=\sum_{j}g_{j}$