A polyatomic gas at pressure 'P', having volume 'V' expands isothermally to a volume ' 3 V ' and then adiabatically to a volume ' 24 V '. The final pressure of gas is (for moderate temperature changes)

The gas undergoes isothermal expansion from volume $V$ to $3V$ at constant temperature. Since $PV = \text{constant}$ for isothermal processes, the pressure reduces from $P$ to $P_2 = P \cdot \frac{V}{3V} = \frac{P}{3}$.

The subsequent adiabatic expansion from volume $3V$ to $24V$ follows $PV^\gamma = \text{constant}$, with $\gamma = \frac{4}{3}$ for polyatomic gases. Using $P_2(3V)^{4/3} = P_3(24V)^{4/3}$:

$P_3 = \frac{P}{3} \cdot \left(\frac{3V}{24V}\right)^{4/3} = \frac{P}{3} \cdot \left(\frac{1}{8}\right)^{4/3} = \frac{P}{3} \cdot \frac{1}{2^{3 \cdot (4/3)}} = \frac{P}{3} \cdot \frac{1}{16} = \frac{P}{48}$

Final pressure: $\frac{P}{48}$