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QPages 34-37: Q62: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q62 Solution: A bucket full of water is placed in a room at 15�C with initial …

A bucket full of water is placed in a room at 15�C with initial relative humidity 40%. The volume of the room is 50 m350 \text{ m}^3. a) How much water will evaporate? b) If the room temperature is increased by 5�C, how much more water will evaporate? The saturation vapour pressure of water at 15�C and 20�C are 1.6 kPa and 2.4 kPa respectively. Use R=8.3 J K−1 mol−1R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:** (a) Mass evaporated = 0.24 kg (b) More water evaporated = 0.65 kg **Step-by-Step Explanation:** (a) At 15�C: saturation pressure = 1.6 kPa, RH = 40%, so actual = 0.64 kPa. Moles of vapour in room:
n=640×508.3×288=13.4 moln = \frac{640 \times 50}{8.3 \times 288} = 13.4 \text{ mol}
Mass = 13.4×18=24113.4 \times 18 = 241 g ≈\approx 0.24 kg. (b) At 20�C: saturation pressure = 2.4 kPa. Moles needed for saturation:
n′=2400×508.3×293=49.3 moln' = \frac{2400 \times 50}{8.3 \times 293} = 49.3 \text{ mol}
Mass = 49.3×18=88749.3 \times 18 = 887 g. Additional water = 887−241=646887 - 241 = 646 g ≈\approx 0.65 kg.

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