What is the pressure of hydrogen in a cylinder of volume 10 litre if its total energy of translation is $7.5…

What is the pressure of hydrogen in a cylinder of volume 10 litre if its total energy of translation is $7.5 \times 10^3 \mathrm{~J}$ ?
  1. $5 \times 10^5 \mathrm{Nm}^{-2}$
  2. $10^6 \mathrm{Nm}^{-2}$
  3. $0.5 \times 10^5 \mathrm{Nm}^{-2}$
  4. $5 \times 10^6 \mathrm{Nm}^{-2}$

Solution

$\begin{aligned} \text { Pressure } & =\frac{2}{3} \times \frac{\text { Kinetic energy }}{\text { Volume }} \\ & =\frac{2 \times 7.5 \times 10^3}{3 \times\left(10 \times 10^{-3}\right)}=5 \times 10^5 \mathrm{~N} / \mathrm{m}^2\end{aligned}$

Asked in: MHT CET 2024 (11 May Shift 2)

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