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Question: Answered & Verified by Expert
A cylinder of capacity 20 litres is filled with $\mathrm{H}_2$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5 \times 10^5 \mathrm{~J}$. The pressure of hydrogen in the cylinder is
PhysicsKinetic Theory of GasesJEE Main
Options:
  • A $2 \times 10^6 \mathrm{~N} / \mathrm{m}^2$
  • B $3 \times 10^6 \mathrm{~N} / \mathrm{m}^2$
  • C $4 \times 10^6 \mathrm{~N} / \mathrm{m}^2$
  • D $5 \times 10^6 \mathrm{~N} / \mathrm{m}^2$
Solution:
1798 Upvotes Verified Answer
The correct answer is: $5 \times 10^6 \mathrm{~N} / \mathrm{m}^2$
$E=\frac{3}{2} P V \Rightarrow P=\frac{2 E}{3 V}=\frac{2}{3} \times \frac{1.52 \times 10^5}{20 \times 10^{-3}}$ $=\frac{10^5}{20 \times 10^{-2}}=5 \times 10^6 \mathrm{~N} / \mathrm{m}^2$

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