Consider an ideal gas confined… - JEE Main 2015 Physics PYQ

JEE Main 2015 — Physics Thermodynamics

2015mcqhard

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:

$(\gamma =\frac{{C}_{P}}{{C}_{v}})$

Official previous-year question

Held on 4 Apr 2015 · Verified 6 Jul 2026.

Options

A
$\frac{\gamma -1}{2}$
B
$\frac{ 3 \gamma + 5 }{ 6 }$
C
$\frac{3\gamma -5}{6}$
D
$\frac{\gamma +1}{2}$

Did you get this right?

Solution

For an adiabatic process $T{V}^{\gamma -1}=$ constant.

We know that average time of collision between molecules

$\tau =\frac{1}{n\pi \sqrt{2}{v}_{\mathrm{rms}}{d}^{2}}$

where, $n=$ number of molecules per unit volume ${V}_{\mathrm{rms}}=$ rms velocity of molecules

As $n\propto \frac{1}{V}$ and ${v}_{\mathrm{rms}}\propto \sqrt{T}$

$\tau \propto \frac{V}{\sqrt{T}}$

Thus, we can write

$n={K}_{1}{V}^{-1}$ and ${V}_{\mathrm{rms}}={K}_{2}{T}^{\frac{1}{2}}$ .

where, ${K}_{1}$ and ${K}_{2}$ are constants.

For adiabatic process, $T{V}^{\gamma -1}=$ constant. Thus, we can write

$\tau \propto V{T}^{-\frac{1}{2}}\propto V{({V}^{1-\gamma })}^{\frac{-1}{2}}$

or $\tau \propto {V}^{\frac{\gamma +1}{2}}$

Your note

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Solution

For an adiabatic process $T{V}^{\gamma -1}=$ constant.

We know that average time of collision between molecules

$\tau =\frac{1}{n\pi \sqrt{2}{v}_{\mathrm{rms}}{d}^{2}}$

where, $n=$ number of molecules per unit volume ${V}_{\mathrm{rms}}=$ rms velocity of molecules

As $n\propto \frac{1}{V}$ and ${v}_{\mathrm{rms}}\propto \sqrt{T}$

$\tau \propto \frac{V}{\sqrt{T}}$

Thus, we can write

$n={K}_{1}{V}^{-1}$ and ${V}_{\mathrm{rms}}={K}_{2}{T}^{\frac{1}{2}}$ .

where, ${K}_{1}$ and ${K}_{2}$ are constants.

For adiabatic process, $T{V}^{\gamma -1}=$ constant. Thus, we can write

$\tau \propto V{T}^{-\frac{1}{2}}\propto V{({V}^{1-\gamma })}^{\frac{-1}{2}}$

or $\tau \propto {V}^{\frac{\gamma +1}{2}}$

Options

Did you get this right?

Solution

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Options

Did you get this right?

Solution

Your note

JEE Main Thermodynamics in other years

More JEE Main Thermodynamics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Optics

Waves & Oscillations

Keep practicing Thermodynamics