adiatomic gas, if it does a work of when a heat of Q is supplied to it is
A)
B) \[\frac{5R}{2}\]
C) \[\frac{10R}{3}\]
D) \[\frac{6R}{3}\]
Correct Answer: C
Solution :
\[dU={{C}_{V}}dT=\left[ \frac{5}{2}R \right]dT\] \[\Rightarrow \] \[dT=\frac{2(dU)}{5R}\] From first law of thermodynamics \[dU=dQ-dW\] \[=Q-\frac{Q}{4}=\frac{3Q}{4}\] Now, molar heat capacity \[C=\frac{dQ}{dT}=\frac{Q}{\frac{2(dU)}{5R}}=\frac{5RQ}{2\left[ \frac{3Q}{4} \right]}=\frac{10}{3}R\]
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