Question

An ideal gas follows a process described by $pV^{2} =C$ from $(p_{1}, V_{1}, T_{1})$ to $(p_{2},V_{2},T_{2})$ and $C$ is a constant. Then,

• A. if $p_{1} > p_{2}$ then $T_{2} > T_{1}$
• B. if $V_{2} > V_{1}$ then $T_{2} < T_{1}$
• C. if $V_{2} > V_{1}$ then $T_{2} > T_{1}$
• D. if $p_{1} > p_{2}$ then $T_{1} > T_{2}$

Answer 1

Answer: (B)

$pV^{2}=C$
$\Rightarrow \left(\frac{nRT}{V}\right) .V^{2} =C $
[$\therefore $ for an ideal gas,$ pV = nRT$]
$\Rightarrow TV=\frac{C}{nR}=$a constant
$\therefore T\propto\frac{1}{V}$
so, if $ V_{2}>V_{2}$ then $T_{2} < T_{1} $