# The total number of air molecules in a room of capacity 20 m³ at a temperature of 27°C and 1 atm pressure is

Q: The total number of air molecules in a room of capacity 20 m³ at a temperature of 27°C and 1 atm pressure is

Sol: Given; Volume(V) = 20m³

Temperature (T) = 27 + 273 = 300K

Pressure (P) = 1 atm = 1.01 × 105 Pa

Total number of air molecules $\large = \frac{P V}{K_B T}$

$\large = \frac{1.01 \times 10^5 \times 20}{1.38 \times 10^{-23} \times 300}$

= 4.87 × 1026