Question

Pressure exerted by a perfect gas is equal to

• A. Mean kinetic energy per unit volume
• B. Half of the mean kinetic energy per unit volume
• C. Two thirds of mean kinetic energy per unit volume
• D. One third of mean kinetic energy per unit volume

Answer 1

Answer: (C)

According to kinetic theory of gases,
$C=\sqrt{\frac{3RT}{M}}$;
$C=$ Root mean square velocity
or, $C^2=\frac{3RT}{M}$
or, $\frac{C^2}{3}=\frac{RT}{M}=\frac{PV}{W}$
$[\therefore PV=nRT]$
or, $P=\frac{w\times C^2}{3V}=\frac{2}{3V}\left(\frac{1}{2}w{C}^2\right)$
or, $P=\frac{2}{3}$ of mean kinetic energy per unit volume.