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:
The peak temperature of the cycle.