JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as \(V ^q\), where \(V\) is the volume of the gas. The value of \(q\) is \(\left( {\gamma = \frac{{{C_P}}}{{{C_V}}}} \right)\)
- A \(\frac{{3\gamma - 5}}{6}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\)
- B \(\;\frac{{\gamma + 1}}{2}\)
- C \(\;\frac{{\gamma - 1}}{2}\)
- D \(\;\frac{{3\gamma + 5}}{6}\)
Answer & Solution
Correct Answer
(B) \(\;\frac{{\gamma + 1}}{2}\)
Step-by-step Solution
Detailed explanation
\(\tau = \frac{1}{{\sqrt 2 \pi {d^2}\left( {\frac{N}{V}} \right)\sqrt {\frac{{3RT}}{M}} }}\) \(\tau \propto \frac{V}{{\sqrt T }}\) \(As,\,T{V^{\gamma - 1}} = K\) \(So,\,\tau \propto {V^{\gamma + 1/2}}\) \(Therefore,\,q = \frac{{\gamma + 1}}{2}\)
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