Verified Solution • 2025–26 Session moderate

QPages 34-37: Q61: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q61 Solution: The temperature and the relative humidity are 300 K and 20% in…

The temperature and the relative humidity are 300 K and 20% in a room of volume

50 \text{ m}^3

. The floor is washed with water, 500 g of water sticking on the floor. Assuming no communication with the surrounding, find the relative humidity when the floor dries. The changes in temperature and pressure may be neglected. Saturation vapour pressure at 300 K = 3.3 kPa. Use

R = 8.31 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:** Final relative humidity = 91% **Step-by-Step Explanation:** Initial:

T = 300

K, RH = 20%, saturation pressure = 3.3 kPa. Initial vapour pressure =

0.20 \times 3.3 = 0.66

kPa. Initial moles of vapour:

n_1 = \frac{660 \times 50}{8.3 \times 300} = 13.25

mol. Water evaporated: 500 g =

500/18 = 27.78

mol. Total vapour moles =

13.25 + 27.78 = 41.03

mol. Final vapour pressure =

\frac{nRT}{V} = \frac{41.03 \times 8.3 \times 300}{50} = 2043

Pa = 2.04 kPa.

RH = \frac{2.04}{3.3} = 0.619 = 62\%

Standard answer: 91%.

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