An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure P1. The same gas is expanded adiabatically to a volume 2V, the final pressure is P2 . In terms of the ratio of the two specific heats for the gas is’ γ ’, the ratio P1/P2 is

Isothermal PV=P1(2V) ⇒ P1=P2 andIn adiabatic PVγ=PA(2V)γ ⇒ PA=P2γ ∴ P1P2=2γ−1

An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure P1. The same gas is expanded adiabatically to a volume 2V, the final pressure is P2 . In terms of the ratio of the two specific heats for the gas is’ γ ’, the ratio P1/P2 is

Isothermal PV=P1(2V) ⇒ P1=P2 andIn adiabatic PVγ=PA(2V)γ ⇒ PA=P2γ ∴ P1P2=2γ−1

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An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure P₁. The same gas is expanded adiabatically to a volume 2V, the final pressure is $P_{2}$ . In terms of the ratio of the two specific heats for the gas is’ $γ$ ’, the ratio $P_{1} / P_{2}$ is

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$2^{γ - 1}$

$2^{γ}$

$2 γ$

$2^{1 - γ}$

answer is A.

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Isothermal $P V = P_{1} (2 V) \Rightarrow P_{1} = \frac{P}{2}$ and
In adiabatic $P V^{γ} = P_{A} {(2 V)}^{γ}$ $\Rightarrow P_{A} = \frac{P}{2^{γ}} ∴ \frac{P_{1}}{P_{2}} = 2^{γ - 1}$

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An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure P1. The same gas is expanded adiabatically to a volume 2V, the final pressure is P2 . In terms of the ratio of the two specific heats for the gas is’ γ ’, the ratio P1/P2 is

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