Two moles of an ideal monoatomic gas is heated from $27°C\text{\hspace{0.17em} to }627°C$ , reversibly and isochorically. The entropy of the gas is

For reversible and isochoric process the entropy change of gas is given by,

$\mathrm{\Delta S}={\mathrm{nC}}_{\mathrm{v}}\ln \left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)$

for monoatomic gas, ${\mathrm{C}}_{\mathrm{v}}=\frac{3}{2}\mathrm{R}$

$\begin{array}{r}\mathrm{n}=2\text{ mole }\\ {\mathrm{T}}_1={27}^{\circ }\mathrm{C}=27+273=300\mathrm{K}\\ {\mathrm{T}}_2={627}^{\circ }\mathrm{C}=627+272=900\mathrm{K}\\ \mathrm{\Delta S}=2\times \frac{3}{2}\mathrm{Rln}\left(\frac{900}{300}\right)\\ \mathrm{\Delta S}=3\mathrm{Rln}3\end{array}$