Problem 1 In a Rankine power system (Figure 1), 1.5 kg s¹ of steam leaves the turbine as saturated vapor at 0.51 bar. The steam is condensed to saturated liquid by passing it over the tubes of a shell-and-tube heat exchanger, while liquid water, having an inlet temperature of Tei = 280 K, is passed through the tubes. The condenser contains 100 thin-walled tubes, each of 10-mm diameter. The total water flow rate through the tubes is 15 kg s-1. The average convection coefficient associated with condensation on the outer surface of the tubes may be approximated as ho = 5000 W m-2K-1. Approximate property values for the liquid water are cp = 4178 Jkg-¹K-¹, = 700 x 10-6 kgs-¹m-¹, k = 0.628 W m-¹K-¹, and Pr = 4.6. Condenser Turbine Water Tep Saturated Steam liquid from boiler to pump Figure 1: Rankine power system. Questions: (a) What is the water outlet temperature? (b) What is the required tube length (per tube)? (c) After extended use, deposits accumulating on the inner and outer tube surface provide a cumu- lative fouling factor of 0.0003 m²K W-1. What is the mass fraction of the vapor condensed for the prescribed inlet conditions and the computed tube length?