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PhysicsNEET 2025Ideal gas equation and kinetic interpretation of pressure

Kinetic Theory

A container has two chambers of volumes V1=2V_1 = 2 litres and V2=3V_2 = 3 litres separated by a partition made of a thermal insulator. The chambers contain n1=5n_1 = 5 and n2=4n_2 = 4 moles of ideal gas at pressures p1=1p_1 = 1 atm and p2=2p_2 = 2 atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of:

  1. A.1.3 atm
  2. B.1.6 atm✓
  3. C.1.4 atm
  4. D.1.8 atm

Solution

Temperature is the same throughout (no heat exchange with outside, ideal gases). Final P=n1+n2V1+V2RTP = \frac{n_1 + n_2}{V_1 + V_2}RT and RT=p1V1n1=p2V2n2RT = \frac{p_1V_1}{n_1} = \frac{p_2V_2}{n_2}. Using p1V1+p2V2=(n1+n2)RTp_1V_1 + p_2V_2 = (n_1 + n_2)RT: P=1×2+2×35=1.6P = \frac{1\times2 + 2\times3}{5} = 1.6 atm.

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