A methane-fired microturbine based on the regenerative gas turbine cycle employs a centrifugal compressor with a polytropic efficiency of 85%, a radial inflow turbine with a polytropic efficiency of 87% and a recuperator with an effectiveness of 0.75. The pres-sure loss is 10% divided equally between the high- and low-pressure sides. To avoid the use of exotic materials in the hot section, the combustor was limited to an equiva-lence ratio of 0.2, with a resulting combustor exit temperature of 1200K when the com-pressor inlet temperature is 298K. The working fluid can be assumed to be air with k = 1.4 with a cp = 1.025 kJ/kg-K in the compressor, 1.050 kJ/kg-K on both sides of the re-cuperator, and 1.075 kJ/kg-K in the combustor and turbine. The fuel is available as a gas at atmospheric pressure and 298K and must be pumped to a pressure that is 10% higher than the combustor exit pressure using a small compressor whose adiabatic efficiency is 60% (this is parasitic power to be subtracted from engine output). The specific heat, cp, of methane is 2.35 kJ/kg-K, and its k = 1.28. The combined mechanical and electrical efficiency of the turbine and the electric generator is 90%. If the compressor pressure ratio is 5:1, and the net power output is 500 kWe, compute the overall efficiency of the turbo-generator set, accounting for mechanical, electric and parasitic losses. Calculate the air and fuel flow rates under these conditions and estimate the exergy efficiency of the combustor, accounting for the methane pumping parasitic power.