The entropy change when two moles of ideal monoatomic gas is heated from 200 to 300° C reversibly and isochorically? ·

For constant volume,

$\mathrm{\Delta }{S}_{\mathrm{sys}}=n{C}_v\ln \left(\frac{T_2}{T_1}\right)$

We have given that,

$\mathrm{n}=2\text{ moles }$

$C_v=3/2R$  (from monoatomic gas)

$\begin{array}{r}{T}_2={200}^{\circ }\mathrm{C}=(200+273)\mathrm{K}=473\mathrm{K}\\ T_1={300}^{\circ }\mathrm{C}=(300+273)\mathrm{K}=573\mathrm{K}\end{array}$

Put the values in the formula as,

$\begin{array}{l}\therefore \mathrm{\Delta S}=2\times \frac{3}{2}\mathrm{R}\times \ln \left(\frac{573}{473}\right)\\ \Rightarrow \mathrm{\Delta S}=3\mathrm{Rln}\left(\frac{573}{473}\right)\end{array}$