Question

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

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

Answer 1

Answer: (D)

$\text{P}\text{V}^{3}=$ constant polytropic process with $\text{n} \, = \, 3$
$\text{C}=\text{C}_{\text{v}}+\frac{\text{R}}{1 - \text{n}}$
For monoatomic gas : $\text{C}_{\text{v}}=\frac{3 \text{R}}{2}$
$\text{C}=\frac{3 \text{R}}{2}+\frac{\text{R}}{1 - 3}$
$=\frac{3 \text{R}}{2}-\frac{\text{R}}{2}$
$=\frac{2 \text{R}}{2}$
$\text{C}=\text{R}$