Question

A cylinder of capacity $20L$ is filled with $H_2$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5\times {10}^{5}J$. The pressure of hydrogen in the cylinder is

• A. $2\times {10}^{6}N/m^2$
• B. $3\times {10}^{6}N/m^2$
• C. $4\times {10}^{6}N/m^2$
• D. $5\times {10}^{6}N/m^2$

Answer 1

The correct option is D $5\times {10}^{6}N/m^2$

The degree of freedom of a diatomic gas ($H_2$) is =5

out of which 3 are related to translatory motion and 2 are rotatory.

according to Maxwell's Law of Equipartition Energy total energy is equally shared among all degree of freedom.

if total energy is $E_t$, then translatory motion energy $E=\frac{3}{5}{E}_t$

$\frac{3}{5}{E}_t=1.5\times {10}^5$

$E_t=2.5\times {10}^{5}J$

total energy of diatomic gas $E_t=\frac{5}{2}PV$

$P=\frac{2E_t}{5V}$

$V=20\times {10}^{-3}$ because $1m^3=1000L$

$P=\frac{2\times 2.5\times {10}^5}{5\times 20\times {10}^{-3}}$

solve for $P$

$P=5\times {10}^{6}N/m^2$

answer is D.