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: γ = C P C v

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Correct answer: D. γ + 1 2

Average time of collision t = m e a n f r e e p a t h ( λ ) a v e r a g e s p e e d ( v ) t ∝ λ v ∵ λ ∝ 1 n o . o f m o l e c u l e s p e r u n i t v o l u m e λ ∝ 1 N v ⇒ λ ∝ V And v ¯ ∝ v r v So average time ∴ t a v g ∝ V V 1 - r 2 t a v g ∝ V 1 - 1 - r 2 t a v g ∝ V 1 + r 2 ∴ q = 1 + r 2

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: γ = C P C v

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