Kinetic Theory NCERT Solutions Class 11 Physics - Solved Exercise Question 13.6

Question 13.6:
Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m3 at a temperature of 27 °C and 1 atm pressure.
Solution:
Volume of the room, V = 25.0 m3
Temperature of the room, T = 27°C = 300 K
Pressure in the room, P = 1 atm = 1 × 1.013 × 105 Pa
The ideal gas equation relating pressure (P), Volume (V), and absolute temperature (T) can be written as:
PV = kBNT
Where,
KB is Boltzmann constant = 1.38 × 10–23 m2 kg s–2 K–1
N is the number of air molecules in the room
∴ N = PV / kBT
= 1.013 X 105 X 25 / (1.38 X 10-23 X 300)
= 6.11 X 1026 molecules
Therefore, the total number of air molecules in the given room is 6.11 × 1026.

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