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]
$PV=P^{\prime }\times 2V$
$\frac{P}{2}=P^{\prime }$
$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
[for adiabatic]
$\frac{P}{2}\times (2V{)}^{5/3}=P_2(V{)}^{5/3}$
$[\gamma$ for neon $=5/3]$
$P=P_2\cdot (2{)}^{-2/3}$
Fractional decrease $=\frac{P_2-P}{P_2}$
$=\frac{P_2-P_2\cdot (2{)}^{-2/3}}{P_2}=1-2^{-2/3}$