Neon gas of a given mass expands isothermally to double volume. What should be the further fractional decrease in pressure, so that the gas when adiabatically compressed from that state, reaches the original state?
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(a)
$P_1 V_1=P_2 V_2$ [for isothermal]
$P V=P \times 2 V$
$\frac{P}{2}=P^{\prime}$
$P_1 V_1^\gamma=P_2 V_2^\gamma$ [for adiabatic]
$\frac{P}{2} \times(2 V)^{5 / 3}=P_2(V)^{5 / 3}$ $[\gamma$ for neon $=5 / 3]$
$P=P_2 \cdot(2)^{-2 / 3}$
Fractional decrease $=\frac{P_2-P}{P_2}=\frac{P_2-P_2 \cdot(2)^{-2 / 3}}{P_2}=1-2^{-2 / 3}$
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