Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 20207 JanuaryEvening Shift

Exam: JEE Main
Year: 2020
Date: 7 January
Shift: Evening Shift
Subject: Physics
Chapter: Thermodynamics

JEE Main 2020 · 7 January · Evening Shift · Physics · Thermodynamics

Under an adiabatic process, the volume of an ideal gas gets...

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecule changes from

{τ}_{1}

to

{τ}_{2}

. If

\dfrac{{C}_{P}}{{C}_{v}} = \gamma

for this gas then a good estimate for

\dfrac{{τ}_{2}}{{τ}_{1}}

is given by

Options

A $2$
B $\dfrac{1}{2}$
C{ $\left(\dfrac{1}{2}\right)}^{\gamma}$
D ${\left(\dfrac{1}{2}\right)}^{\dfrac{\gamma + 1}{2}}$

Correct answer

D. ${\left(\dfrac{1}{2}\right)}^{\dfrac{\gamma + 1}{2}}$

Step-by-step solution

Relaxation time

\left(τ\right) ∝ \dfrac{V}{\sqrt{T}}

And

T ∝ \dfrac{1}{{V}^{\gamma - 1}}

τ ∝ {V}^{1 + \dfrac{\gamma - 1}{2}}

τ ∝ V\dfrac{1 + \gamma}{2}

\dfrac{{τ}_{f}}{{τ}_{i}} = {\left(\dfrac{2V}{V}\right)}^{\dfrac{\gamma + 1}{2}}

\dfrac{{τ}_{f}}{{τ}_{i}} = {\left(2\right)}^{\dfrac{\gamma + 1}{2}}

Practice Thermodynamics on Quantrex Academy →

More from Thermodynamics

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process ( ab )… JEE Advanced 2026 As shown in the figure, five Carnot engines, each with efficiency η and same number of… JEE Advanced 2026 Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and… JEE Advanced 2026 One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston… JEE Main 2026 Initial pressure and volume of a monoatomic ideal gas are P and V . The change in… JEE Main 2026 A cylinder with adiabatic walls is closed at both ends and is divided into two… JEE Main 2026 Two closed vessels of same volume are joined through a narrow tube and both vessels are… JEE Main 2026 A certain gas is isothermally compressed to ((1)/(3))^ rd of its initial volume ( V_o = 3… JEE Main 2026 Full Thermodynamics list All JEE Main PYQs