MHT CET · Physics · Kinetic Theory of Gases

The pressure exerted by an ideal gas on the walls of a container is

A ${[\frac{1}{3}]}^{r d}$ of kinetic energy per unit volume of a gas
B ${[\frac{2}{3}]}^{r d}$ of kinetic energy per unit volume of a gas
C ${[\frac{3}{4}]}^{t h}$ of kinetic energy per unit volume of a gas
D $\frac{3}{2} \times$ kinetic energy per unit volume of a gas

Verified Solution

Answer & Solution

Correct Answer

(B) ${[\frac{2}{3}]}^{r d}$ of kinetic energy per unit volume of a gas

Step-by-step Solution

Detailed explanation

The pressure exerted by the gas on the walls of container is $P=\frac{1}{3} \rho v^2$
$P=\frac{1}{3} \rho v^2=\frac{1}{3} \frac{m}{V} \cdot v^2 \times \frac{2}{2}=\frac{2}{3} \frac{K E}{\text { Volume }}$

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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