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A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above piston is l 1 , and that below the piston is l 2 , such that l 1 > l 2 . Each part of the cylinder contains n moles of an ideal gas at equal temperature T . If the piston is stationary, its mass m will be gi

Options

  1. AR T n g l 1 - 3 l 2 l 1 l 2
  2. Bn R T g l 1 - l 2 l 1 l 2
  3. Cn R T g 1 l 2 + 1 l 1
  4. DR T g l 2 l 1 + l 2 l 1 l 2

Correct answer

B. n R T g l 1 - l 2 l 1 l 2

Step-by-step solution

P 1 + m g A = P 2 ⇒ n R T l 1 A + m g A = n R T l 2 A ⇒ m = n R T g 1 l 2 - 1 l 1 = n R T g l 1 - l 2 l 1 l 2

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