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JEE Main 20246 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Morning Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2024 · 6 April · Morning Shift · Physics · Kinetic Theory of Gases

The specific heat at constant pressure of a real gas obeying P...

The specific heat at constant pressure of a real gas obeying PV2=RTP V^2=R T equation is:

Options

  1. AR3+CV\frac{R}{3}+C_V
  2. BCV+RC_V+R
  3. CCV+R2VC_V+\frac{R}{2 V}
  4. DRR

Correct answer

C. CV+R2VC_V+\frac{R}{2 V}

Step-by-step solution

dQ=du+dWCdT=CVdT+PdV∴PV2=RTP= constant P(2VdV)=RdTPdV=RdT2V\begin{aligned} & \mathrm{dQ}=\mathrm{du}+\mathrm{dW} \\ & \mathrm{CdT}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}+\mathrm{PdV} \\ & \therefore \mathrm{PV}^2=\mathrm{RT} \\ & \mathrm{P}=\text{ constant } \\ & \mathrm{P}(2 \mathrm{VdV})=\mathrm{RdT} \\ & \mathrm{PdV}=\frac{\mathrm{RdT}}{2 \mathrm{ V}} \\ & \end{aligned}Put in equation (1) C=CV+R2V\mathrm{C}=\mathrm{C}_{\mathrm{V}}+\frac{\mathrm{R}}{2 \mathrm{ V}}
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