One mole of a diatomic gas does a work $\frac{\mathrm{Q}}{3}$, when the amount of heat supplied is 'Q'. In…

One mole of a diatomic gas does a work $\frac{\mathrm{Q}}{3}$, when the amount of heat supplied is 'Q'. In this process, the molar heat capacity of the gas is
  1. $\frac{15 \mathrm{R}}{4}$
  2. $\frac{9 \mathrm{R}}{4}$
  3. $\frac{7 \mathrm{R}}{4}$
  4. $\frac{3 \mathrm{R}}{4}$

Solution

The amount of heat required to increase the internal energy is $\left(\mathrm{Q}-\frac{\mathrm{Q}}{3}\right)=\frac{2}{3} \mathrm{Q}$ For a diatomic gas, the amount of heat required to increase the internal energy is $C_{v}=\frac{5}{2} R$ $\begin{array}{l} \therefore \frac{2}{3} Q=\frac{5}{2} R \\ \therefore Q=\frac{15}{4} R \end{array}$

Asked in: MHT CET 2020 (13 Oct Shift 2)

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