Question

The molar heat capacity in a process of a diatomic gas, if it does a work of $\frac{Q}{4}$ when a heat of Q is supplied to it is

• A. $\frac{2R}{5}$
• B. $\frac{5R}{2}$
• C. $\frac{10R}{3}$
• D. $\frac{6R}{7}$

Answer 1

Answer: (C)

$dU=C_{V}dT=\left[\frac{5}{2}R\right]dT$ $\Rightarrow$ $dT=\frac{2(dU)}{5R}$ From first law of thermodynamics $dU=dQ-dW=Q-\frac{Q}{4}=\frac{3Q}{4}$ Now, molar heat capacity $C=\frac{dQ}{dT}=\frac{Q}{\frac{2(dU)}{5R}}=\frac{5RQ}{2\left[\frac{3Q}{4}\right]}=\frac{10}{3}R$