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{3 R T}{M}} $;
$ C=$ Root mean square velocity
or, $C ^{2}=\frac{3 RT }{ M }$
or, $\frac{C^{2}}{3}=\frac{R T}{M}=\frac{P V}{W}$
$[\therefore P V=n R T]$
or, $P=\frac{w \times C^{2}}{3 V}=\frac{2}{3 V}\left(\frac{1}{2} w C^{2}\right)$
or, $P=\frac{2}{3}$ of mean kinetic energy per unit volume.