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. $T{V}^{2/5}=constant$
• B. $V{P}^{5/3}=constant$
• C. $T{P}^{-2/5}=constant$
• D. $P{T}^{2/5}=constant$

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;
$P{V}^{5/3}=\text{constant}$
$T{V}^{2/3}=\text{constant}$
$T^{5/3}{P}^{-2/3}=\text{constant}$
$\Rightarrow T{P}^{-2/5}=\text{constant}$