Question

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

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

Answer 1

Answer: (A)

$R$

$P{V}^{\ast }=$ constant (Polytropic process)

Heat capacity in polytropic process is given by

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

Given that $P{V}^3=constant\Rightarrow x=3$ ......(1)

Also gas is monoatomic so $C_V=\frac{3}{2}R$ .......(2)

By formula

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

Hence, option A is correct