A gas turbine power plant operates under the Brayton cycle, which is non-ideal due to heat losses from the compressor and turbine. The cycle uses air as the working fluid, has a pressure ratio of 12:1 and a mass flow rate of 100 kg/s. The cycle has a net power output of 50,000 kW and a thermal efficiency of 38%.

Air at 300 K and 100 kPa enters the compressor, which has an unknown isentropic efficiency and losses heat at the rate of 1000 kW. The turbine has an isentropic efficiency of 86.1% and a heat loss rate of 1000 kW. If the turbine were isentropic, the working fluid would leave at 963.3 K. Hint: When working with the isentropic efficiency definition, use the exact form of the definition with the ratio of works/powers.

Assume that the heat transferred into the system originates from a high temperature reservoir whose temperature is equal to the maximum temperature of the cycle. Also assume that all heat rejection processes are to a low temperature reservoir with a temperature of 300 K. Using the properties of air at 300 K, find:

a) The power into the compressor.
b) The peak temperature of the cycle.
c) The total power out of the turbine.
d) The back work ratio.
e) The second law efficiencies of the compressor and turbine.
f) The rate of exergy destruction for each process in the cycle. Where does the maximum rate of exergy destruction occur?
g) The rate of useful work that the cycle could perform.