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