Question

Determine the mass of air contained in a pressurised container if the temperature is 150° C, the pressure is 170kPa (gauge) and the volume is 3 litres.

(Take R = 287J/kgK for air)

Answer 1

Given:

Temperature of air, Ta = 1500C = 150 + 273 = 423K

Gauge Pressure,Pg = 170kPa

Volume of the container,V = 3 Litres = 3 x 10-3 m3

R = 287 J/kgK

Let Patm = 101.325kPa

Solution:

We know that, Ideal gas equation, Pv = mRT

Where , - Density of air

Therefore we can write the gas equation as --------- (1)

We know that,

Absolute Pressure, Pabs = Gauge Pressure(Pg) + Atmospheric Pressure(Patm)

Pabs = 170 + 101.325 = 271.325 kPa

Substituting all the values in equation (1) we get,

271.325 x 103 = x 287 x 423

= 2.235 kg/m3

Mass of air in the container,

m = Density of air x Volume of the container

m = 2.235 x 3 x 10-3 = 6.705 x 10-3 kg (or) 6.705 grams

Mass of air in the container, m = 6.705 g