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Determine the density, specific gravity, and mass of the air in a room whose dimensions are 4m × 5m × 6m at 100 kPa and 25° C.(a) 1.16 kg/m^3, 0.00116, 140 kg(b) 1.17 kg/m^3, 0.00117, 140 kg(c) 1.15 kg/m^3, 0.00115, 140 kg(d) 1.14 kg/m^3, 0.00114, 140 kg |
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Answer» Correct choice is (b) 1.17 kg/m^3, 0.00117, 140 kg To elaborate: At specified conditions, air can be treated as ideal gas. The gas constant of air is R = 0.287 k Pa-m^3/Kg K The density of the air is determined from the ideal-gas relation, P = ρ R T to be ρ = P/RT = (100 kPa)/((0.287 k Pa-m^3/Kg K) (25+273.15)K) = 1.17 kg/ m^3 Then the specific gravity of the air becomes SG = (ρ)/ρH2O = (1.17 kg/m^3)/(1000 kg/m^3) = 0.00117 Finally, the volume and mass of the air in the room are V = (4m) (5m) (6m) = 120 m^3 m = ρV = (1.17 kg/m^3) (120 m^3) = 140 kg. |
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