8-86 Consider a family of four, with each person taking a 6-minute shower every morning. The average flow rate through the shower head is 10 L/min. City water at 15C is heated to 55C in an electric water heater and tempered to 42C by cold water at the T-elbow of the shower before being routed to the shower head. Determine the amount of exergy destroyed by this family per year as a result of taking daily showers. Take To 25C. 8-87 Ambient air at 100 kPa and 300 K is compressed isentropically in a steady-flow device to 1 MPa. Determine (a) the work input to the compressor, (b) the exergy of the air at the compressor exit, and (c) the exergy of compressed air after it is cooled to 300 K at 1 MPa pressure. 8-88 Cold water (c, = 4.18 kJ/kg C) leading to a shower enters a well-insulated, thin-walled, double-pipe, counter-flow heat exchanger at 15C at a rate of 0.25 kg/s and is heated to 45C by hot water (c, = 4.19 kJ/kg C) that enters at 100C at a rate of 3 kg/s. Determine (a) the rate of heat transfer and (b) the rate of exergy destruction in the heat exchanger. Take T = 25C. To Hot water 3 kg/s 100C +45C Cold water 0.25 kg/s | 15C FIGURE P8-88 8-89 Outdoor air (c = 1.005 kJ/kg C) is to be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. Air enters the heat exchanger at 95 kPa and 20C at a rate of 0.8 m/s. The combustion gases (c, = 1.10 kJ/kg C) enter at 180C at a rate of 1.1 kg/s and leave at 95C. Determine the rate of heat transfer to the air and the rate of exergy destruction in the heat exchanger. Air 95 kPa 20C 0.8 m/s FIGURE P8-89 Exhaust gases 1.1 kg/s 95C 8-90 A well-insulated shell-and-tube heat exchanger is used to heat water (c, = 4.18 kJ/kg C) in the tubes from 20 to 70C at a rate of 4.5 kg/s. Heat is supplied by hot oil (c, = 2.30 kJ/kg - C) that enters the shell side at 170C at a rate of 10 kg/s. Disregarding any heat loss from the heat exchanger, determine (a) the exit temperature of oil and (b) the rate of exergy destruction in the heat exchanger. Take To = 25C.