Question

A 1.6 m³ tank is filled with air at a pressure of 5 bar and a temperature of 100°C. The air is then let off to the atmosphere through a valve. Assuming no heat transfer, determine the work obtainable by utilising the kinetic energy of the discharge air to run a frictionless turbine. 

Take : Atmospheric pressure = 1 bar ; 

c_p for air = 1 kJ/kg K ; 

c_v for air = 0.711 kJ/kg K.

Answer 1

Initial volume of air, V₁ = 1.6 m³ 

Initial pressure of air, p₁ = 5 bar = 5 × 10⁵ N/m² 

Initial temperature of air, T₁ = 100 + 273 = 373 K 

Final pressure of air, p₂ = 1 bar = 1 × 10⁵ N/m² 

Now, initial quantity of air in the tank before discharge

Assuming that system undergoes a reversible adiabatic expansion

where T₂ is the final temperature of air in the tank.

T₂ = 373 × 0.631 = 235.4 K (i.e., finally in the line)

The final quantity of air remaining in the tank is

With Q = 0, kinetic energy is found from,

= 7.47 × 0.771 × 373 – 2.368 × 0.711 × 235.4 – (7.47 – 2.368) × 1 × 235.4 

= 2148.24 – 396.33 – 1201 = 550.9 kJ.