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JEE Main 2015 · Thermodynamic Processes

Thermodynamic Processes question from JEE Main 2015

Q228JEE Main 2015Difficult

Thermodynamic Processes

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,V^{q}, where VV is the volume of the gas. The value of qq is: (γ=CpCv)\left(\gamma = \frac{C_p}{C_v}\right)

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Answer: (a)

  1. τ=λvrms\tau = \frac{\lambda}{v_{rms}} with λ∝V\lambda \propto V and vrms∝Tv_{rms} \propto \sqrt{T}, so τ∝VT\tau \propto \frac{V}{\sqrt{T}}.
  2. Adiabatic: T∝V1−γT \propto V^{1-\gamma}, so τ∝V1+γ−12=Vγ+12\tau \propto V^{1 + \frac{\gamma-1}{2}} = V^{\frac{\gamma+1}{2}}.
  3. So q=γ+12q = \frac{\gamma+1}{2}, answer (a).
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