Answer to Question #152625 in Classical Mechanics for Isurini Sirisena

Question

Estimate the mass of air in this room.

Answer 1

The molar mass of air is 28.97 g/mol.

For example, volume of room will be $40 \; m^3 \; (5 \; m \times 4 \; m \times 2 \; m).$

$V = 40 \; m^3 = 40000 \; L$

The temperature will be 20 ºC, the pressure 1 atm.

T = 20 + 273 = 293 K

p = 1 atm

Ideal gas law:

pV = nRT

R=0.082058 L×atm/(K×mol)

$n = \frac{pV}{RT} \\ n = \frac{1 \times 40000}{0.082058 \times 293} = 1663.68 \;mol \\ m_{air} = 1663.68 \times 28.97 \\ = 48196.8 \;g \\ = 48.19 \; kg$

Answer: 48.19 kg