A bucket full of water is placed in a room at 15^ C with an initial relative humidity of 40 % . The volume of the room is 50 m ^3 . The saturation vapour pressures of water at 15^ C and 20^ C are 1.6 kPa and 2.4 kPa respectively. Assuming the room has already reached saturation at 15^ C , if the room temperature is subsequently increased by 5^ C , how much additional water will evaporate?

Step-by-step solution

Let the mass of water vapour in the room at saturation at 15^ C be m₁ . Using the ideal gas equation PV = nRT , we have: n₁ = P₁ V R T₁ m₁ = P₁ V M R T₁ Substituting the given values ( P₁ = 1.6 kPa = 1600 Pa , V = 50 m ^3 , T₁ = 288 K , M = 18 g/mol , R = 8.314 J/(mol K) ): m₁ = 1600 50 18 8.314 288 601.4 g When the temperature is increased to 20^ C ( 293 K ), the new saturation vapour pressure is P₂ = 2.4 kPa = 2400 Pa . The mass of water vapour at saturation at 20^ C is: m₂ = P₂ V M R T₂ m₂ = 2400 50 18 8.314 293