A) \[\frac{2}{5}R\]
B) \[\frac{10}{3}R\]
C) \[\frac{5}{3}R\]
D) \[\frac{6}{5}R\]
Correct Answer: B
Solution :
From the fist law of thermodynamic \[dU=dQ-dW\] \[=Q-\frac{Q}{4}=\frac{3Q}{4}\] Also, \[dU={{C}_{V}}dT=\left( \frac{5}{2}R \right)dT\] For diatomic gas, \[dT=\left( \frac{2}{5}R \right)dU\] \[=\frac{2}{5R}\times \frac{3Q}{4}\] \[=\frac{3Q}{10R}\] Molar heat capacity \[C=\frac{dQ}{dT}=\frac{Q}{3Q/10R}\] \[=\frac{10R}{3}\]
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