Question

An ideal gas expands according to the law $P{V}^{3/2}=\text{constant}$. We conclude

• A. The adiabatic exponent of the gas $K=1.5$
• B. The molar heat capacity $C=C_v-2R$
• C. Temperature increases during the process
• D. Such a process is not feasible

Answer 1

The correct option is B The molar heat capacity $C=C_v-2R$

We know
equation of polytropic process $P{V}^n=\text{Constant}$
Here $n=\frac{3}{2}$
Molar heat capacity-
$C=C_v+\frac{R}{1-n}=C_v+\frac{R}{1-\frac{3}{2}}=C_v-2R$
Given:
$P{V}^{\frac{3}{2}}=\text{Constant}$
Using $PV=nRT$
$T{V}^{\frac{1}{2}}=\text{Constant}$
$\Rightarrow$ As $V$ increases $T$ decreases