Our space program requires a portable engine to generate electricity for a space station. It is proposed to use sodium (T_c  = 2300 K; P_c = 195 bar; ω = 0; C_P/R  2.5) as the working fluid in a customized form of a “Rankine” cycle. The high-temperature stream is not superheated before running through the turbine. Instead, the saturated vapor (T = 1444 K, P^sat = 0.828 MPa) is run directly through the (100% efficient, adiabatic) turbine. The rest of the Rankine cycle is the usual. That is, the outlet stream from the turbine passes through a condenser where it is cooled to saturated liquid at 1155 K (this is the normal boiling temperature of sodium), which is pumped (neglect the pump work) back into the boiler.

(a) Estimate the quality coming out of the turbine.

(b) Compute the work output per unit of heat input to the cycle, and compare it to the value for a Carnot cycle operating between the same T_H and T_C.