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JEE Main 201323 AprilOnline
Exam
JEE Main
Year
2013
Date
23 April
Mode
Online
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2013 · 23 April · Online · Physics · Kinetic Theory of Gases

This question has Statement-1 and Statement-2. Of the four choices...

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume. Statement 2: A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.

Options

  1. AStatement-1 is true, Statement- 2 is true and Statement −2-2 is the correct explanation of Statement-1.
  2. BStatement-1 is true, Statement-2 is false.
  3. CStatement-1 is true, Statement-2 is true but Statement-2 is not the correct explanation of Statement-1.
  4. DStatement-1 is false, Statement-2 is true.

Correct answer

C. Statement-1 is true, Statement-2 is true but Statement-2 is not the correct explanation of Statement-1.

Step-by-step solution

Internal energy of a system is the energy possessed by the system due to molecular motion and molecular configuration. Internal energy u=uk+upu=u_k+u_p For an ideal gas there is no molecular attraction up=0\mathrm{u}_{\mathrm{p}}=0 ∴\therefore Internal energy u=uk\mathrm{u}=\mathrm{u}_{\mathrm{k}} (i.e., internal kinetic energy)andu=uk=32μRTand \mathrm{u}=\mathrm{u}_{\mathrm{k}}=\frac{3}{2} \mu \mathrm{RT} At constant pressure (ΔQ)P=μCpΔT(\Delta \mathrm{Q})_{\mathrm{P}}=\mu \mathrm{C}_{\mathrm{p}} \Delta \mathrm{T} At constant volume (ΔQ)v=μCvΔT(\Delta \mathrm{Q})_{\mathrm{v}}=\mu \mathrm{C}_{\mathrm{v}} \Delta \mathrm{T} As C P>CV∴(ΔT)P<(ΔT)V_{\mathrm{P}}>\mathrm{C}_{\mathrm{V}} \quad \therefore \quad(\Delta \mathrm{T})_{\mathrm{P}} < (\Delta \mathrm{T})_{\mathrm{V}}
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