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Concepts Of Physics MCQ Edition [Volume 2]PhysicsKinetic Theory of Gases

A faulty barometer contains a certain amount of air and saturated water vapour. It reads 74.0 cm when the atmospheric pressure is 76.0 cm of mercury, and it reads 72.10 cm when the atmospheric pressure is 74.0 cm of mercury. The saturation vapour pressure at the air temperature is 1.0 cm of mercury. Determine the length of the barometer tube above the mercury level in the reservoir.

Options

  1. A129.1 cm
  2. B9.11 cm
  3. C91.1 cm
  4. D110.1 cm

Correct answer

C. 91.1 cm

Step-by-step solution

Let L be the length of the barometer tube above the mercury level in the reservoir. Let P_ a be the pressure of the air inside the tube and P_ v be the saturation vapour pressure. The atmospheric pressure P_ atm balances the mercury column h and the pressure inside the tube: P_ atm = h + P_ a + P_ v P_ a = P_ atm - h - P_ v For the first case: P_ atm1 = 76.0 cm , h₁ = 74.0 cm , P_ v = 1.0 cm P_ a1 = 76.0 - 74.0 - 1.0 = 1.0 cm The length of the air column is L₁ = L - 74.0 . For the second case: P_ atm2 = 74.0 cm , h

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