Consider a gas turbine engine operating on a Brayton cycle with a regenerator. Air enters the compressor of this engine at $100$ kPa and $30$ oC$.$ The compressor pressure ratio is $10$; the maximum cycle temperature is $800$ oC; and the cold air stream leaves the regenerator $10$ oC cooler than the hot air stream at the inlet of the regenerator. Assume both the compressor and the turbine to be isentropic$.($a$)$ Sketch the T$-$s diagram for the cycle $($b$)$ determine the rates of heat addition and rejection for this cycle when it produces $115$ kW$.$ Answers: $258$ kW$,143$ kW