1. Tardigrade
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  3. Physics
  4. 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 (γ =(Cp/Cv))

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Q. 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 $\bigg(\gamma =\frac{C_p}{C_v}\bigg)$

JEE MainJEE Main 2015Thermodynamics

Solution:

mean free path
$\lambda=\frac{1}{\sqrt{2}\, \pi d ^{2} n}$
$n =\frac{\text { no. of molecules }}{\text { volume }}$
$v _{\text {avg. }} \propto \sqrt{ T }\,\,\,\,\,\,\,T .V ^{\gamma-1}= C$
$t =\frac{\lambda}{ V _{\text {avg. }}} \propto \frac{ V }{\sqrt{ T }} \,\,\,\,\,\,\,v \rightarrow$ is volume
$\frac{ V }{\sqrt{\frac{ C }{ v ^{ r -1}}}} \propto V ^{\frac{\gamma+1}{2}}$
$v^{q} \propto v^{\frac{\gamma+1}{2}}$
$q =\frac{\gamma+1}{2}$