A gas obeying the equation of state pV = RT u | vedclass

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(A) The process equation is $pV^{5/3} \cdot e^{-pV/E_0} = C_1$.Taking the natural logarithm on both sides: $\ln(p) + \frac{5}{3} \ln(V) = \ln(C_1) + \

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approaches a constant value

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(A) The process equation is $pV^{5/3} \cdot e^{-pV/E_0} = C_1$.Taking the natural logarithm on both sides: $\ln(p) + \frac{5}{3} \ln(V) = \ln(C_1) + \frac{pV}{E_0}$.Differentiating with respect to $V$: $\frac{1}{p} \frac{dp}{dV} + \frac{5}{3V} = \frac{1}{E_0} \left( p + V \frac{dp}{dV} ight)$.Rearranging terms to find $\frac{dp}{dV}$: $\frac{dp}{dV} \left( \frac{1}{p} - \frac{V}{E_0} ight) = \frac{p}{E_0} - \frac{5}{3V}$.Using $pV = RT$,we have $p = \frac{RT}{V}$. Substituting this,the isothermal compressibility $k = -\frac{1}{V} \frac{dV}{dp}$ is derived.As $T 	o \infty$,the terms involving $\frac{1}{RT}$ approach zero.Thus,$k = -\frac{1}{V} \frac{dV}{dp} = \frac{1/p - V/E_0}{p/E_0 - 5/3V} \cdot \frac{1}{V} \approx 	ext{constant}$ as $T 	o \infty$.

Column-$I$	Column-$II$
$(i)$ Adiabatic process	$(a)$ Constant temperature
$(ii)$ Isolated system	$(b)$ No exchange of energy and matter
$(iii)$ Isothermal change	$(c)$ First law of thermodynamics
$(iv)$ Law of conservation of energy	$(d)$ No transfer of heat only

$A$. Steam engine	$I$. Magnetic confinement of plasma
$B$. Electron microscope	$II$. Laws of thermodynamics
$C$. Non-reflecting coatings	$III$. Wave nature of electrons
$D$. Tokamak	$IV$. Interference of light

$A$ gas obeying the equation of state $pV = RT$ undergoes a hypothetical reversible process described by the equation $pV^{5/3} \exp \left(-\frac{pV}{E_0}\right) = C_1$,where $C_1$ and $E_0$ are dimensioned constants. Then,for this process,the thermal compressibility at high temperature

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