Physics | MHT CET 2016 | Discussion Page

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) $\frac{3}{2}\times$ kinetic energy per unit volume of a gas

Option B

According to kinetic theory of gases, the pressure exerted by the gas on the walls of container is

p= p₀+p₁+p₂

i.e, $p= p_{0}+\frac{1}{3}8v^{2}+3gh$

For a container,

$p_{1}=\frac{1}{3}\rho v^{2}= \frac{1}{3}\frac{m}{v}.v^{2}\times\frac{2}{2}=\frac{2}{3}.\frac{1}{2}mv^{2}.\frac{1}{v}$

= $\frac{2}{3v} KE $ $\left[\because KE= \frac{1}{2}mv^{2}\right]$

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