Verified Solution • 2025–26 Session moderate

QPages 34-37: Q58: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q58 Solution: On a winter day, the outside temperature is 0�C and relative…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume the relative humidity stays the same or that the water‑vapour amount changes with temperature; remember that when air is heated without moisture exchange the vapor’s partial pressure (or absolute humidity) remains constant, so RH must be recomputed as $RH_{new}=p_{v}/p_{sat}(T_{new})$, not by scaling the original RH directly.

On a winter day, the outside temperature is 0�C and relative humidity 40%. The air from outside comes into a room and is heated to 20�C. What is the relative humidity in the room? The saturation vapour pressure at 0�C is 4.6 mm of mercury and at 20�C it is 18 mm of mercury.

Step-by-Step Verified Solution

**Answer:** Relative humidity in room = 10.2% **Step-by-Step Explanation:** Outside: T=0�CT = 0�\text{C}, RH = 40%, saturation pressure = 4.6 mm Hg. Partial pressure of water vapour = 0.40×4.6=1.840.40 \times 4.6 = 1.84 mm Hg. When air enters the room and is heated to 20�C, the absolute humidity remains the same (partial pressure of vapour unchanged). Inside: T=20�CT = 20�\text{C}, saturation pressure = 18 mm Hg.
RHroom=1.8418=0.102=10.2%RH_{room} = \frac{1.84}{18} = 0.102 = 10.2\%

All Questions in this Chapter

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