Question

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

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

Answer 1

The correct option is B $3\times {10}^6{\text{N/m}}^2$

Given:
Volume of cylinder, $V=20\text{L}=20\times {10}^{-3}{\text{m}}^3$
Degree of freedom of diatomic gas is $5$ out of which $3$ are translatory and $2$ are rotational.
If total energy is $E_t$, then according to law of equipartition of energy, translatory motion energy $=\frac{3}{5}{E}_t$.

Given, average translational kinetic energy, $KE=1.5\times {10}^5\text{J}=\frac{3}{5}{E}_t$
So, total K.E, $\Rightarrow E_t=\frac{5\times 1.5\times {10}^5}{3}=2.5\times {10}^5\text{J}$
To find:
Pressure of hydrogen in the cylinder, $P=?$
$P=\frac{2E_t}{5V}\Rightarrow P=\frac{2\times 2.5\times {10}^5}{20\times {10}^{-3}\times 5}$
[ $f=5$ for diatomic gases ]
$\Rightarrow P=5\times {10}^6{\text{N/m}}^2$