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MHT CET 2024 (11 May, Shift 2) · Pressure & Kinetic Energy of a Gas

Pressure & Kinetic Energy of a Gas question from MHT CET 2024 (11 May, Shift 2)

Q16MHT CET 2024 · 11 MAY · SHIFT 2Medium

Pressure & Kinetic Energy of a Gas

What is the pressure of hydrogen in a cylinder of volume 10 litre if its total energy of translation is 7.5×103 J7.5 \times 10^{3}\text{ J}?

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Answer: (a)

  1. P=23EVP = \frac{2}{3}\frac{E}{V}
  2. V=10V = 10 L =10−2= 10^{-2} m3^3, so EV=7.5×10310−2=7.5×105\frac{E}{V} = \frac{7.5 \times 10^{3}}{10^{-2}} = 7.5 \times 10^{5} J/m3^3
  3. P=23×7.5×105=5×105P = \frac{2}{3} \times 7.5 \times 10^{5} = 5 \times 10^{5} N m−2^{-2}
  4. So the answer is (a) 5×1055 \times 10^{5} N m−2^{-2}.
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