First slide

Different type of processes

Question

One mole of an ideal monoatomic gas undergoes a process described by the equation PV³ = constant.The heat capacity of the gas during this process is :

Moderate

A

2R
B

R
C

$\frac{3}{2} R$
D

$\frac{5}{2} R$

Solution

PV^x= constant (Polytropic process)
Heat capacity in polytropic process is given by $[C = C_{V} + \frac{R}{1 - x}]$
Given that PV³ = constant $\Rightarrow$ x = 3
Also gas is monoatomic so $C_{V} = \frac{3}{2} R$
By formula
$C = \frac{3}{2} R + \frac{R}{1 - 3} = \frac{3}{2} R - \frac{R}{2} = R$

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