Question 2.1: Density, Specific Gravity, and Mass of Air in a Room Determi...
Density, Specific Gravity, and Mass of Air in a Room
Determine the density, specific gravity, and mass of the air in a room whose dimensions are 4 m × 5 m × 6 m at 100 kPa and 25°C (Fig. 2–6).
The density, specific gravity, and mass of the air in a room are to
be determined.
Assumptions At specified conditions, air can be treated as an ideal gas.
Properties The gas constant of air is R = 0.287 kPa⋅m^3/kg⋅K.
Analysis The density of the air is determined from the ideal-gas relation P = \rho RT to be
\rho =\frac{P}{RT} = \frac{100 kPa}{(0.287 kPa.m^3/kg.K)(25 + 273.15 K)}= 1.17 kg/m^3
Then the specific gravity of the air becomes
SG = \frac{\rho }{\rho _{H_2O}} = \frac{1.17 kg/m^3}{1000 kg/m^3} = 0.00117
Finally, the volume and the mass of the air in the room are
V = (4 m)(5 m)(6 m) = 120 m^3
m = ρV = (1.17 kg/m^3)(120 m^3) = 140 kg
Discussion Note that we converted the temperature to (absolute) unit K from ( relative) unit °C before using it in the ideal-gas relation.