Question

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?

• A. $1-2^{-2 / 3}$
• B. $1-3^{1 / 3}$
• C. $2^{1 / 3}$
• D. $3^{2 / 3}$

Answer 1

Answer: (A)

$P_{1} V_{1}=P_{2} V_{2}$
[for isothermal]
$P V=P' \times 2 V$
$\frac{P}{2}=P'$
$P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma}$
[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 $=\frac{P_{2}-P}{P_{2}}$
$=\frac{P_{2}-P_{2} \cdot(2)^{-2 / 3}}{P_{2}}=1-2^{-2 / 3}$