Question

Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure is

• A. $\left[\frac{1}{3}\right]^{rd}$ kinetic energy per unit volume of a gas
• B. $\left[\frac{2}{3}\right]^{rd}$ kinetic energy per unit volume of a gas
• C. $\left[\frac{3}{4}\right]^{th}$ kinetic energy per unit volume of a gas
• D. $\frac{3}{3} \times$ kinetic energy per unit volume of a gas

Answer 1

Answer: (B)

Kinetic energy of the gas $K =\frac{1}{2} mv _{ rms }^{2}$
$R m s$ velocity of gas molecules $v _{ rms }=\sqrt{\frac{3 R T}{m}}$ $\therefore K =\frac{1}{2} m \cdot \frac{3 RT }{ m }=\frac{3}{2} RT$
From ideal gas equation, $RT = PV$
$\Rightarrow K =\frac{3}{2} PV$
Thus we get pressure of the gas $P =\frac{2}{3} \frac{ K }{ V }$