A proposed simple gas turbine will produce power at a rate

Chapter 13, Problem 13.4D

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A proposed simple gas turbine will produce power at a rate of 0.5 MW by burning fuel with 200% theoretical air in the combustor. Air temperature and pressure at the compressor inlet are 298 K and 100 kPa, respectively. Fuel enters the combustor at 298 K, while products of combustion consisting of \(\mathrm{CO}_{2}\), \(\mathrm{H}_{2} \mathrm{O}\), \(\mathrm{O}_{2}\), and \(\mathrm{N}_{2}\) exit the combustor with no significant change in pressure. Metallurgical considerations require the turbine inlet temperature to be no greater than 1500 K. Products of combustion exit the turbine at 100 kPa. The compressor has an isentropic efficiency of 85%, while the turbine isentropic efficiency is 90%. Three fuels are being considered: methane (\(\mathrm{CH}_{4}\)), ethylene (\(\mathrm{C}_{2} \mathrm{H}_{4}\)), and ethane (\(\mathrm{C}_{2} \mathrm{H}_{6}\)). With the aim of minimizing fuel use, recommend a fuel, turbine inlet temperature, and compressor pressure ratio for the gas turbine. Summarize your findings in a report supported by well-documented sample calculations and a full discussion of the thermodynamic modeling used.