An air compressor is allowed to run until the gage pressure

An air compressor is allowed to run until the gage pressure in the compressor tank is 500 kPa. The compressor is transported to a truck that has a portable air tank that is initially at atmospheric pressure. The compressor tank is connected to the portable tank. What will be the equilibrium mass of air in each tank (kg)? What will be the equilibrium gage pressure in each tank (kPa)? The transfer process occurs with constant temperatures throughout (20 degree C), and the tanks are cylindrical.

Solution

P₁ = Pressure inside the air compressor = 500kPa

P₂ = Pressure inside the portable tank = 1.01325 bar

V₁= Volume of the air compressor = pi*0.3²*1/4 = 0.07068 m³

V₂ = Volume of the portable tank = pi*0.15²*0.5/4 = 0.0088357 m³

T₁ = T₂

m₁ = (P₁ V₁) / (RT₁) = 0.42029 kg = Initial mass inside the compressor

m₂ = P₂V₂ / RT₂ = 0.01064 kg = initial mass inside tank.

P₃ = ( P₁V₁ + P₂V₂ ) / (V₁ + V₂) = 455.701 kPa

Hence final Pressure inside the compressor and cylindrical tank will be 455.701 kPa so that equilibrium is maintained.

m₃ = final mass inside compressor = P₃V₁/(RT₁) = 0.38305 kg

m₄ =  final mass inside tank = P₃V₂/(RT₂) = 0.04785 kg