Question

Certain perfect gas is found to obey $P{V}^{3/2}=constant$ during an adiabatic process. If such a gas at initial temperature T is adiabatically compressed to half the initial volume, its final temperature will be

• A. $\sqrt{2}T$
• B. $2T$
• C. $2\sqrt{2}T$
• D. $4T$

Answer 1

Answer: (A)

$\sqrt{2}T$

Using the ideal gas law, P is directly proportional to $\frac{T}{V}$
Substituting this value,
$T{V}^{0.5}=constant$
Thus, when the volume is halved, we raise the temperature by $\sqrt{2}$ times.