Q140 / 160 · AP EAMCET 2023 (15 May Shift 1) · Physics

A vessel of volume 10 liters is filled with $\mathrm{H}_2$ gas. The total average translational kinetic energy of its molecules is $4.5 \times 10^5 \mathrm{~J}$. The pressure of hydrogen in the vessel is

  • A
    $3 \times 10^6 \mathrm{Nm}^{-2}$
  • Correct answer
    B
    $30 \times 10^6 \mathrm{Nm}^{-2}$
  • C
    $30 \times 10^4 \mathrm{Nm}^{-2}$
  • D
    $3 \times 10^4 \mathrm{Nm}^{-2}$

Solution

Pressure, $P=\frac{2}{3} \frac{\mathrm{E}}{\mathrm{V}}=\frac{2}{3} \times \frac{4.5 \times 10^5}{10 \times 10^{-3}}=30 \times 10^6 \mathrm{Nm}^{-2}$

Hence, the correct answer is option: 'B'.

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