Determine the total mass of nitrogen ideal gas in kg require

Determine the total mass of nitrogen (ideal gas), in kg, required to inflate all four tires of a vehicle, each to a gage pressure of 1.8 bar at a temperature of 25 degree C. The volume of each tire is0.6 m^3, and the atmospheric pressure is 1 atm or 0.01025 bar. (1 bar = 10^5 N/m^2)

Solution

The pressure in the tire is = atmospheric pressure + gauge pressure

                                          = 1.013 + 1.8 bar   [ 1 atm = 1.013 bar]

                                         = 2.813 bar = 2.813 x 100 kPa = 281.3 kPa

Universal gas constant for Nitrogen, R = (8.314 / 28) = 0.297 kJ/kg-K

Temperature, T = (25+273) K = 298 K, Volume of a tire, V = 0.6 m

Now, PV = mRT    [ m = masss of Nitrogen in one tire]

m = PV / RT = (281.3 x 0.6) / (0.297 x 298) = 1.91 kg

So, total mass in all four tires = (1.91 x 4) kg = 7.64 kg.

The mass of nitrogen required to inflate all four tires is 7.64 kg.