Kinetic Theory

JEE Main level, single correct, medium

115 of 168

Question 115 of 168

An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PVn=P{V}^{n}= constant, then n is given by (Here CP{C}_{P} and CV{C}_{V} are molar specific heat at constant pressure and constant volume, respectively) :

Show answer and solution

Answer: (D) n=C−CPC−CVn=\dfrac{C-{C}_{P}}{C-{C}_{V}}

PVn=kP{V}^{n}=k

C=Cv+R1−nC={C}_{v}+\dfrac{R}{1-n} ; C−Cv=R1−nC-{C}_{v}=\dfrac{R}{1-n}

1−n=RC−Cv1-n=\dfrac{R}{C-{C}_{v}} ; n=1−RC−Cvn=1-\dfrac{R}{C-{C}_{v}}

n=C−Cv−RC−Cvn=\dfrac{C-{C}_{v}-R}{C-{C}_{v}} ; n=C−Cv−(Cp−Cv)C−Cvn=\dfrac{C-{C}_{v}-\left({C}_{p}-{C}_{v}\right)}{C-{C}_{v}}

n=C−Cv−Cp+CvC−Cvn=\dfrac{C-{C}_{v}-{C}_{p}+{C}_{v}}{C-{C}_{v}} ; n=C−CpC−Cvn=\dfrac{C-{C}_{p}}{C-{C}_{v}}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

More Physics practice

JEE Main Physics practice question on Kinetic Theory (Degree of Freedom and Specific Heat), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.