Physics · Thermodynamics

JEE Main 2024 — 5 April, Shift 2 — Question 44

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_{P}}{C_{V}}$ for the gas is :

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

Answer: C

Step-by-step solution

$\mathrm{P} \propto \mathrm{T}^{3}$

$\mathrm{PT}^{-3}=$ constant $\because \frac{\mathrm{PV}}{\mathrm{T}}=\mathrm{nR}=$ constant from ideal gas equation

(P) $(\mathrm{PV})^{-3}=$ constant $\mathrm{P}^{-2} \mathrm{~V}^{-3}=$

cosntant $\because$ Process equation for adiabatic process is

$\mathrm{PV}^{\mathrm{y}}=$

constant Comparing equation (1) and (2)

$\frac{C_{P}}{C_{V}}=y=\frac{3}{2}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 5 April, Shift 2
Subject: Physics
Chapter: Thermodynamics
Topic: Different Thermodynamic Processes