Verified Solution • 2025–26 Session moderate

QPages 34-37: Q53: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q53 Solution: A glass contains some water at room temperature 20�C.…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often confuse the room temperature (20°C) with the condensation temperature (10°C) when determining the actual vapor pressure. Remember that condensation begins when the surface temperature equals the dew point, so the partial pressure of water vapor in the air is equal to the saturation vapor pressure at the condensation temperature (10°C), not the room temperature.

A glass contains some water at room temperature 20�C. Refrigerated water is added to it slowly. when the temperature of the glass reaches 10�C, small droplets condense on the outer surface. Calculate the relative humidity in the room. The boiling point of water at a pressure of 17.5 mm of mercury is 20�C and at 8.9 mm of mercury it is 10�C.

Step-by-Step Verified Solution

**Answer:** Relative humidity = 50.9% **Step-by-Step Explanation:** At 20�C, saturation vapour pressure = 17.5 mm Hg. At 10�C, saturation vapour pressure = 8.9 mm Hg. Condensation occurs on the outer surface when the glass temperature reaches 10�C. This means the partial pressure of water vapour in the room equals the saturation pressure at 10�C:
Pvapour=8.9 mm HgP_{vapour} = 8.9 \text{ mm Hg}
RH=8.917.5=0.509=50.9%RH = \frac{8.9}{17.5} = 0.509 = 50.9\%

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