# 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 - Physics

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 1

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)/(k_BT)

= (1.013xx10^5xx25)/(1.38xx10^(-23)xx300) = 6.11 xx 10^(26) molecules

Therefore, the total number of air molecules in the given room is 6.11 × 1026.

#### Solution 2

Here, Volume of room, V= 25.0 m^3, temperature, T = 27 ^@C = 300 K and

Pressure, P = 1 "atm" = 1.01 xx 10^5 Pa

According to gas equation, PV = muRT = muN_A.k_BT

Hence, total number of air molecules in the volume of given gas

N = mu.N_A = PV/K_BT

:. N = (1.01 xx 10^5 xx25.0)/((1.38 xx 10^(-23))xx300) = 6.1 xx 10^(26)

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#### APPEARS IN

NCERT Class 11 Physics Textbook
Chapter 13 Kinetic Theory
Q 6 | Page 334