Question

A simple ideal Brayton cycle operates with air with minimum and maximum temperatures of 27°C and 727°C. It is designed so that the maximum cycle pressure is 2000 kPa and the minimum cycle pressure is 100 kPa. Determine the net work produced per unit mass of air each time this cycle is executed and the cycle’s thermal efficiency. Use constant specific heats at room temperature.

Answer 1

Using isentropic relations for an ideal gas:

T2 = T1(P2/P1)^(k-1)/k =

300K(2000kPa/100kPa)^0.4/1.4 = 706.1K

T4 = T3(P4/P3)^(k-1)/k =

1000K(100kPa/2000kPa)^0.4/1.4 = 424.9K

Apply the first law tot he constant-pressure heat addition process produces:

q in = h3-h2 = cp(T3-T2) =

1.005kJ/kgK * (1000 - 706.1)K = 295.4 kJ/kg

q out = h4 - h1 = cP(T4-T1) =

1.005kJ/kgK * (424.9 - 300)K= 125.5 kJ/kg

Net work production:

wnet = q in - q out =

295.4 - 1125.5 = 169.9 kJ/kg

Thermal efficiency:

w net / q in =

169.9 kJ/kg / 295.4 kJ/kg = 0.575