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 Vq, where V is the volume of the gas. The value of q is :

Engineering

Physics

Thermodynamics

Question

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 :

$(γ = \frac{C_{p}}{C_{v}})$

$\frac{3 γ + 5}{6}$

$\frac{γ + 1}{2}$

$\frac{3 γ - 5}{6}$

$\frac{γ - 1}{2}$

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$Δt = \frac{Δℓ}{v}$

TV^γ–1 = C

T = CV^–γ+1

$∆$ t $\propto$ VT^–1/2

^{$= V \times {CV}^{\frac{γ - 1}{2}}$}

^{$= V^{1 + \frac{γ - 1}{2}}$}

^{$= V^{\frac{γ + 1}{2}}$}