KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 95 of 120

Marks: +1, -0

A gas obeying the equation of state PV = RT undergoes a hypothetical reversible process described by the equation,

\PV^{5/3} \exp(-\PV/\E_0)=c_1

where

c_1

and

E_0

are dimensioned constants. Then, for this process, the thermal compressibility at high temperature

Solution:

\PV^{5/3}=c_1e^{\PV/\E_0}

\ln \P+5/3\ln \V=\ln c_1+\PV/E_0

\dP/\P+5/3\dP/\V=0+{\PdV+\VdP}/\E_0

\dV/\dP={1/P-V/E_0}/{\P-5/{3\V}}

c=-1/\V\dV/\dP={[1/\E_0-1/\PV]}/{[\P-5/{3\V}]}

At very high temperature c

=1/\E_0

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