Consider a simple gas turbine power plant. Air at ambient conditions enters the air compressor at point 1 and exits after compression at point 2.

Consider a simple gas turbine power plant. Air at ambient conditions enters the air compressor at point 1 and exits after compression at point 2. The hot air enters the combustion chamber (CC) into which fuel is injected, and hot combustion gases exit (point 3) and pass through a gas turbine to produce shaft power. The hot gas expands in the gas turbine to point 4. Natural gas (with a volumetric composition of ) is injected into the combustion chamber with a mass flow rate of 2 kg/s. The compressor pressure ratio is 7, the gas turbine inlet temperature is 1400 K and the compressor isentropic efficiency and gas turbine isentropic efficiency are 0.83 and 0.87, respectively. If the net output power of this power plant is 15 MW, and there is no pressure drop in the combustion chamber and heat loss in the compressor and gas turbine;(1) Determine the fuel-to-air ratio, and the molar fractions of the combustion gases.(2) Find the specific physical and chemical exergy values at all points. (3) For a reference state of and , determine the exergy destruction rate and exergy efficiency of the all components as well as the overall cycle. (4) If the compressor pressure ratio varies while other parameters are fixed, show the variation of system exergy efficiency with compressor pressure ratio for various gas turbine isentropic efficiencies. (5) If the gas turbine inlet temperature (GTIT) varies, show the variation of system exergy efficiency and total exergy destruction with GTIT. (6) With reasonable assumptions of the cost parameters, determine the objective functions for optimizing this gas turbine power plant.