MHT CET · Physics · Kinetic Theory of Gases
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
- A \(\frac{15 \mathrm{R}}{4}\)
- B \(\frac{9 \mathrm{R}}{4}\)
- C \(\frac{7 \mathrm{R}}{4}\)
- D \(\frac{3 \mathrm{R}}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{15 \mathrm{R}}{4}\)
Step-by-step Solution
Detailed explanation
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 \(C_{v}=\frac{5}{2} R\)
\(\begin{array}{l}
\therefore \frac{2}{3} Q=\frac{5}{2} R \\
\therefore Q=\frac{15}{4} R
\end{array}\)
\(\left(\mathrm{Q}-\frac{\mathrm{Q}}{3}\right)=\frac{2}{3} \mathrm{Q}\)
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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