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Question: Answered & Verified by Expert
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
PhysicsKinetic Theory of GasesJEE Main
Options:
  • A $\frac{15 \mathrm{R}}{4}$
  • B $\frac{9 \mathrm{R}}{4}$
  • C $\frac{7 \mathrm{R}}{4}$
  • D $\frac{3 \mathrm{R}}{4}$
Solution:
1153 Upvotes Verified Answer
The correct answer is: $\frac{15 \mathrm{R}}{4}$
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 $C_{v}=\frac{5}{2} R$
$\begin{array}{l}
\therefore \frac{2}{3} Q=\frac{5}{2} R \\
\therefore Q=\frac{15}{4} R
\end{array}$

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