An ideal gas turbine power cycle Brayton operates with air e

An ideal gas turbine power cycle (Brayton) operates with air entering the compressor at 100 kPa and 15C. The pressure ratio is 12 and the turbine inlet temperature is 1100 C. Assuming a cold air standard (specific heats are constant at the 300K values), determine the compressor work, turbine work, and cycle thermal efficiency. Ans. -300 kJ/kg, 700 kJ/kg, 51%

Solution

During compression T2 / T1 = (P2 / P1)^(n-1)/n

T2 / (15+273) = 12^(1.4-1)/1.4

T2 = 585.8 K

For ideal Brayton cycle, T3 / T4 = T2 / T1

(1100 + 273) / T4 = 585.8 / (15+273)

T4 = 675 K

Compressor work = Cp*(T1 - T2)

= 1.005* ((15+273) - 585.8)

Compressor work = -299.29 kJ/kg

Turbine work = Cp*(T3 - T4)

= 1.005* ((1100+273) - 675)

Turbine work = 701.49 kJ/kg

Net work done = Turbine work + Compressor work

= 701.49 + (-299.29)

Net work done = 402.2 kJ/kg

Heat input = Cp*(T3 - T2)

= 1.005*((1100+273) - 585.8)

Heat input = 791.14 kJ/kg

Thermal eff = Net work done / Heat input

= 402.2 / 791.14

Thermal eff = 0.508 or 50.8%