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Question

A cylinder of capacity 20 L is filled with H2 gas. The total average kinetic energy of translatory motion of its molecules is 1.5×105 J. The pressure of hydrogen in the cylinder is

A
2×106 N/m2
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B
3×106 N/m2
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C
4×106 N/m2
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D
5×106 N/m2
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Solution

The correct option is B 3×106 N/m2
Given:
Volume of cylinder, V=20 L=20×103 m3
Degree of freedom of diatomic gas is 5 out of which 3 are translatory and 2 are rotational.
If total energy is Et, then according to law of equipartition of energy, translatory motion energy =35Et.

Given, average translational kinetic energy, KE=1.5×105 J=35Et
So, total K.E, Et=5×1.5×1053=2.5×105 J
To find:
Pressure of hydrogen in the cylinder, P=?
P=2Et5VP=2×2.5×10520×103×5
[ f=5 for diatomic gases ]
P=5×106 N/m2

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