Physics - Heat & Thermo Question with Solution | TestHub

Given, $V\propto \frac{1}{T}$, or $VT=constant$.

For one mole ideal gas, $PV=RT$.

Since $VT=constant$, we can write $T=\frac{k}{V}$ for some constant $k$.

Substituting this into the ideal gas equation: .

So, $P{V}^2=C$.

The molar specific heat for a polytropic process $P{V}^x=constant$ is given by:

$C=C_V+\frac{R}{1-x}$

For a monoatomic gas, $C_V=\frac{3}{2}R$

Comparing this with $P{V}^x=constant$, we find $x=2$.

$C=\frac{3}{2}R+\frac{R}{1-2}$

$C=\frac{3}{2}R-R$

$C=\frac{1}{2}R$

$n=2$