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

Pure water vapour is enclosed in a vessel of volume 10 cm ^3 at a relative humidity of 40 % . The vapour is slowly compressed isothermally. Determine the volume of the vapour at which condensation starts.

Options

  1. A6 cm ^3
  2. B4 cm ^3
  3. C25 cm ^3
  4. D2.5 cm ^3

Correct answer

B. 4 cm ^3

Step-by-step solution

Relative humidity is given by RH = P P_s 100 % , where P is the partial pressure of water vapour and P_s is the saturated vapour pressure. Given RH = 40 % , the initial pressure of the vapour is P₁ = 0.4 P_s . Condensation begins when the pressure of the vapour reaches the saturated vapour pressure, so the final pressure is P₂ = P_s . Since the process is isothermal, temperature is constant. Using Boyle's law for the water vapour: P₁ V₁ = P₂ V₂ Substituting the given values: 0.4 P_s 10 = P_s V₂ V₂ = 4 cm ^3 Thus, c

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