Question

In a cubical vessel are enclosed n molecules of a gas each having a mass m and an average speed v. If $l$ is the length of each edge of the cube, the pressure exerted by the gas will be

• A. $\frac{nm{v}^2}{l^3}$
• B. $\frac{n{m}^{2}r}{2l^3}$
• C. $\frac{mn{v}^2}{3l^3}$
• D. $\frac{nmv}{2l}$

Answer 1

Answer: (C)

$\frac{mn{v}^2}{3l^3}$

The thermal energy of gas will be equal to the kinetic energy. Hence,

$n\left(\frac{1}{2}m{v}^2\right)=\frac{3}{2}NRT=\frac{3}{2}P\left(l^3\right)$ N being number of moles of gas.

$P=\frac{mn{v}^2}{3l^3}$

Answer is option C.