2.9 A closed-cycle gas turbine is to be used in conjunction with a gas-cooled nuclear reactor. The working fluid is helium (cp = 5.19 kJ/kg K and y = 1.66). The layout of the plant consists of two-stage compression with intercooling followed by a heat-exchanger; after leaving the cold side of the heat-exchanger the helium passes through the reactor channels and on to the turbine; from the turbine it passes through the hot side of the heat-exchanger and then a precooler before returning to the compressor inlet. The following data are applicable: Compressor and turbine polytropic efficiencies Temperature at LP compressor inlet Pressure at LP compressor inlet 0.88 310 K 14.0 bar 2.0 300 K Compressor pressure ratios (LP and HP) Temperature at HP compressor inlet Mass flow of helium 180 kg/s Reactor thermal output (heat input to gas turbine) 500 MW Pressure loss in precooler and intercooler (each) 0.34 bar Pressure loss in heat-exchanger (each side) 0.27 bar Pressure loss in reactor channels 1.03 bar 700 K Helium temperature at entry to reactor channels Calculate the power output and thermal efficiency, and the heat-exchanger effec- tiveness implied by the data. [214.5 MW, 0.429, 0.782]