A) \[\frac{2}{5}R\]
B) \[\frac{5}{2}R\]
C) \[\frac{10}{3}R\]
D) \[\frac{6}{7}R\]
Correct Answer: C
Solution :
\[dU={{C}_{V}}dT=\left( \frac{5}{2}R \right)dT\]or \[dT=\frac{2(dU)}{5R}\] ?..(i) From first law of thermodynamics \[dU=dQ-dW\]\[=Q-\frac{Q}{4}\]\[=\frac{3Q}{4}\]. Now molar heat capacity \[C=\frac{dQ}{dT}=\frac{Q}{\frac{2(dU)}{5R}}=\frac{5RQ}{2\left( \frac{3Q}{4} \right)}=\frac{10}{3}R\].You need to login to perform this action.
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