A Monoatomic Gas At A Pressure P, Having A Volume V Expands Isothermally To A Volume 2V And Then Adiabatically To A Volume 16V. The Final Pressure Of The Gas Is : (Take γ=5/3)

Isothermal expansion

=\( PV = {P}'(2V) \)

For the isothermal process, PV = constant.

Therefore,

\( {P}’ = \frac{P}{2} \)

According to adiabatic expansion

\( {P}’ (2V) \) \( (2V)^{\gamma} = P_{f} (16V)\gamma \)

For adiabatic process,\( PV^{\gamma} = constant \) \( \frac{P}{2} (2V)^\frac{5}{3} \) \( \Rightarrow P_{f} = (16V)^\frac{5}{3} \) \( \Rightarrow P_{f} = \frac{P}{2} (\frac{2V}{16V)^\frac{5}{3} \) \( \Rightarrow \frac{P}{2}(\frac{1}{8})^\frac{5}{3} \) \( \Rightarrow \frac{P}{2}(\frac{1}{2^{3}})^\frac{5}{3} \) \( \Rightarrow \frac{P}{2}(\frac{1}{2^{5}}) \) \( \Rightarrow \frac{P}{64} \)

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