JEE Main 2020 — Physics Thermodynamics

2020mcqmedium

In an adiabatic process, the density of a diatomic gas becomes $32$ $n$ times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is:

Official previous-year question

Held on 5 Sept 2020 · Verified 6 Jul 2026.

Options

A
$32$
B
$326$
C
$128$
D
$\frac{1}{32}$

Did you get this right?

Solution

Given,

Final density of diatomic gas is ${\rho }_{f}=32n{\rho }_{i}$

Final pressure is ${P}_{f}=n{P}_{i}$

In adiabatic process, equation of state is given by,

$P{V}^{\gamma }=\text{constant}...(1)$

Where, $V$ is the volume, $P$ is the pressure and $\gamma =\frac{7}{5}$ is the ratio of specific heat of diatomic gas

$P{(\frac{m}{\rho })}^{\gamma }=\text{constant}...(2)$ , As $V=\frac{m}{\rho }$

and mass is constant, then the pressure is given by

$\therefore P\propto {\rho }^{\gamma }$

$\Rightarrow \frac{{P}_{f}}{{P}_{i}}={(\frac{{\rho }_{f}}{{\rho }_{i}})}^{\gamma }$

$\Rightarrow \frac{n{P}_{i}}{{P}_{i}}={(\frac{32{\rho }_{i}}{{\rho }_{i}})}^{{}^{7/5}}=(32{)}^{7/5}$

$\therefore n={2}^{7}=128$

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Solution

Given,

Final density of diatomic gas is ${\rho }_{f}=32n{\rho }_{i}$

Final pressure is ${P}_{f}=n{P}_{i}$

In adiabatic process, equation of state is given by,

$P{V}^{\gamma }=\text{constant}...(1)$

Where, $V$ is the volume, $P$ is the pressure and $\gamma =\frac{7}{5}$ is the ratio of specific heat of diatomic gas

$P{(\frac{m}{\rho })}^{\gamma }=\text{constant}...(2)$ , As $V=\frac{m}{\rho }$

and mass is constant, then the pressure is given by

$\therefore P\propto {\rho }^{\gamma }$

$\Rightarrow \frac{{P}_{f}}{{P}_{i}}={(\frac{{\rho }_{f}}{{\rho }_{i}})}^{\gamma }$

$\Rightarrow \frac{n{P}_{i}}{{P}_{i}}={(\frac{32{\rho }_{i}}{{\rho }_{i}})}^{{}^{7/5}}=(32{)}^{7/5}$

$\therefore n={2}^{7}=128$

JEE Main 2020 — Physics Thermodynamics

Options

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Solution

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JEE Main 2020 — Physics Thermodynamics

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