Air at 2.5 bar, 400 K is extracted from a main jet engine compressor for cabin cooling. The extracted air enters a heat exchanger where it is cooled at constant pressure to 300 K through heat transfer with the ambient. It then expands adiabatically to 1.0 bar through a turbine and is discharged into the cabin. The turbine has an isentropic efficiency of 80%.

If the mass flow rate of the air is 2.5 kg/s, determine:

(a) the power developed by the turbine, in kw.
(b) the magnitude of the rate of heat transfer from the air to the ambient, in kw

a) Power developed by the turbine = 132.89 kW

b) magnitude of the rate of heat transfer from the air to the ambient, in kw = 251.25 kW

Explanation:

b) The process is a constant pressure process (Isobaric process)

The constant pressure specific heat of air,

Specific heat ratio for air,

The mass flow rate of air,

P₁ = 2.5 bar, T₁ = 400 K

P₂ = 2.5 bar, T₂ = 300 K

Using the steady flow energy equation:

Therefore, the magnitude of the rate of heat transfer from the air to the ambient, in kw,

a) For the isentropic process:

Power developed by the turbine is given by the relation

Isentropic efficiency,

P₂ = 2.5 bar, T₂ = 300 K

P₃ = 1 bar, = ? where is the isentropic temperature at 100% efficiency

The isentropic relation is given by:

To get the temperature at 80% efficiency, we will use the relation:

T₃ = 244.72 K

Power developed by the turbine is given by the relation:

answer:

50 vo; ts

explanation: