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JIPMER 2004
Exam
JIPMER
Year
2004
Subject
Physics
Chapter
Kinetic Theory of Gases

JIPMER 2004 · Physics · Kinetic Theory of Gases

A cylinder contains 10 kg of gas at pressure of 10^7 ~N / m^2 . The...

A cylinder contains 10 kg of gas at pressure of 107 N/m210^7 \mathrm{~N} / \mathrm{m}^2. The quantity of gas taken out of the cylinder, if final pressure is 2.5×106 N/m22.5 \times 10^6 \mathrm{~N} / \mathrm{m}^2 will be (temperature of gas is constant)

Options

  1. A15.2 kg
  2. B3.7 kg
  3. Czero
  4. D7.5 kg

Correct answer

D. 7.5 kg

Step-by-step solution

Intital mass of the gas m1=10 kgm_1=10 \mathrm{~kg} Initial pressure P1=10 N/m2P_1=10 \mathrm{~N} / \mathrm{m}^2 Final pressure P2=2.5×106 N/m2P_2=2.5 \times 10^6 \mathrm{~N} / \mathrm{m}^2 According to kinetic theory of gases PV=13mc−2P V=\frac{1}{3} m c^{-2} or P∝m\quad P \propto m Hence, P1P2=m1m2\quad \frac{P_1}{P_2}=\frac{m_1}{m_2} or 1072.5×106=10m2\quad \frac{10^7}{2.5 \times 10^6}=\frac{10}{m_2} or m2=2.5 kg\quad m_2=2.5 \mathrm{~kg} Hence, quantity of gas taken out from the cylinder is 10−2.5=7.5 kg10-2.5=7.5 \mathrm{~kg}
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