Question

One mole of an ideal monatomic gas undergoes a process described by the equation $P{V}^3=\text{constant}$. The heat capacity of the gas during this process is

• A. $2R$
• B. $R$
• C. $\frac{3}{2}R$
• D. $\frac{5}{2}R$

Answer 1

The correct option is B $R$

$P{V}^x=\text{constant}$ (Polytropic process)
Heat capacity in polytropic process is given by
$\left(C=C_V+\frac{R}{1-x}\right]$
Given that $P{V}^3=\text{constant}$ $\Rightarrow x=3.....\left(1\right)$
Also, gas is monoatomic $\Rightarrow f=3......\left(2\right)$
By formula
$C=\frac{fR}{2}+\frac{R}{1-x}C=\frac{3}{2}R-\frac{R}{2}=R$