Question

Argon gas is adiabatically compressed to half of its volume. If $P ,$ $V$ and $T$ represent the pressure, volume and temperature of the gaseous system respectively, then the correct equation representing the process is

• A. $TV^{2 / 5}=constant$
• B. $VP^{5 / 3}=constant$
• C. $TP^{- 2 / 5}=constant$
• D. $PT^{2 / 5}=constant$

Answer 1

Answer: (C)

For an adiabatic process,
$P V^{\gamma } = \text{constant}$
$T V^{\gamma - 1} = \text{constant}$
and $T^{\gamma } P^{1 - \gamma } = \text{constant}$
Putting, $\gamma = 5 / 3$ (Argon is a monatomic gas),
now equation becomes;
$P V^{5 / 3} = \text{constant}$
$T V^{2 / 3} = \text{constant}$
$T^{5 / 3} P^{- 2 / 3} = \text{constant}$
$\Rightarrow T P^{- 2 / 5} = \text{constant}$