KVPY SB SX Exam 2011 Question Paper

Question : 94 of 120

Marks: +1, -0

One mole of an ideal gas at initial temperature T. undergoes a quasi-static process during which the volume V is doubled. During the process the internal energy U obeys the equation

U = \a \V^3

, where a is a constant. The work done during this process is

3RT/2
5RT/3
5RT/2
7RT/3

Validate

Solution:

\U = \aV^3

{\fnRT}/2=\aV^2

PV = RT

\PV/\R=\aV^2

\P = \CV^2

\W=∫↖{2V}↙{V}PdV=∫↖{2V}↙{V}CV^2dV

=C/3(8V^3-V^3)={7V^3C}/3

{\fRT}/2=\aV^3

PV = RT

{\fPV}/2=\aV^3

P={2a}/fV^2

C={2a}/fV^2

\W=7/3×\V^3×{2a}/\f

=7/{3\f}\fnRT={7\RT}/3

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