The entropy in terms of internal energy $\{\mathrm{U}-\mathrm{U}(0)\}$, and canonical partition function (Q) is given by $\mathrm{S}=\frac{\mathrm{U}-\mathrm{U}(0)}{\mathrm{T}}+\mathrm{k} \ln \mathrm{Q}$. Assuming that T the atoms are distinguishable, the corresponding expression for a monatomic perfect gas is [Here $\mathrm{n}, \mathrm{m}, \mathrm{N}_{\mathrm{A}}, \mathrm{k}$ and h represent number of moles, mass of atom, Avogadro constant,Boltzmann constant and Planck constant, respectively. $\mathrm{U}(0)$ is internal energy at $\mathrm{T}=0]$. Options:
(a)$\mathrm{S}=\frac{5}{2} \mathrm{nR}+\mathrm{nR} \ln \left\{\left.\mathrm{V}(2 \pi \mathrm{mkT})^{\frac{3}{2}} \right\rvert\, \mathrm{nN}_{\mathrm{A}} \mathrm{h}^{3}\right\}$
(b)$\mathrm{S}=\frac{3}{2} \mathrm{nR}+\mathrm{nR} \ln \left\{\left.\mathrm{V}(2 \pi \mathrm{mkT})^{\frac{3}{2}} \right\rvert\, \mathrm{h}^{3}\right\}$
(c)$\mathrm{S}=\frac{5}{2} \mathrm{nR}+\mathrm{nR} \ln \left\{\left.\mathrm{V}(2 \pi \mathrm{mkT})^{\frac{3}{2}} \right\rvert\, \mathrm{h}^{3}\right\}$
(d)$\mathrm{S}=\frac{3}{2} \mathrm{nR}+\mathrm{nR} \ln \left\{\left.\mathrm{V}(2 \pi \mathrm{mkT})^{\frac{3}{2}} \right\rvert\, \mathrm{nN}_{\mathrm{A}} \mathrm{h}^{3}\right\}$