Physics · Thermodynamics

JEE Main 2024 — 27 January, Shift 2 — Question 42

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{C_{p}}{C_{v}}$ for the gas is :

Option A:
$\frac{5}{3}$
Option B:
$\frac{3}{2}$
Correct
Option C:
$\frac{7}{5}$
Option D:
$\frac{9}{7}$

Answer: B

Step-by-step solution

$\mathrm{P} \propto \mathrm{T}^{3} \Rightarrow \mathrm{PT}^{-3}=$ constan

$t$ $\mathrm{PV}^{\gamma}=$

const $\mathrm{P}\left(\frac{\mathrm{nRT}}{\mathrm{P}}\right)^{\gamma}=$

const $\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma}=$

const $\mathrm{PT}^{\frac{\gamma}{1-\gamma}}=$

const $\frac{\gamma}{1-\gamma}=-3$

$\gamma=-3+3 \gamma$

$3=2 \gamma$

$\gamma=\frac{3}{2}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 27 January, Shift 2
Subject: Physics
Chapter: Thermodynamics
Topic: Different Thermodynamic Processes