MHT CET · Physics · Kinetic Theory of Gases
Let \(\gamma_1\) be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \(\gamma_2\) be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio \(\frac{\gamma_2}{\gamma_1}\) is
- A \(\frac{37}{21}\)
- B \(\frac{27}{35}\)
- C \(\frac{21}{25}\)
- D \(\frac{35}{27}\)
Answer & Solution
Correct Answer
(C) \(\frac{21}{25}\)
Step-by-step Solution
Detailed explanation
For monoatomic gas,
\(
\gamma_1=\frac{5}{3}
\)
For rigid diatomic gas,
\(
\begin{aligned}
\gamma_2 =\frac{7}{5} \\
\therefore \frac{\gamma_2}{\gamma_1} & =\frac{7}{5} \times \frac{3}{5}=\frac{21}{25}
\end{aligned}
\)
\(
\gamma_1=\frac{5}{3}
\)
For rigid diatomic gas,
\(
\begin{aligned}
\gamma_2 =\frac{7}{5} \\
\therefore \frac{\gamma_2}{\gamma_1} & =\frac{7}{5} \times \frac{3}{5}=\frac{21}{25}
\end{aligned}
\)
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