Kinetic Theory

JEE Main level, single correct, medium

19 of 168

Question 19 of 168

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.

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Answer: (C) Statement-1 is true, Statement-2 is true but Statement-2 is not the correct explanation of Statement-1.

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)
and u=uk=32μRT\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}}\gt \mathrm{C}_{\mathrm{V}} \quad \therefore \quad(\Delta \mathrm{T})_{\mathrm{P}} \lt (\Delta \mathrm{T})_{\mathrm{V}}

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