Thermodynamics

274 | Thermodynamicsenters the building at a rate of 35 L/s when the indoors ismaintained at 20°C.5–179 The maximum flow rate of standard shower heads isabout 3.5 gpm (13.3 L/min) and can be reduced to 2.75 gpm(10.5 L/min) by switching to low-flow shower heads that areequipped with flow controllers. Consider a family of four,with each person taking a 5 min shower every morning. Citywater at 15°C is heated to 55°C in an electric water heaterand tempered to 42°C by cold water at the T-elbow of theshower before being routed to the shower heads. Assuming aconstant specific heat of 4.18 kJ/kg · °C for water, determine(a) the ratio of the flow rates of the hot and cold water asthey enter the T-elbow and (b) the amount of electricity thatwill be saved per year, in kWh, by replacing the standardshower heads by the low-flow ones.5–180 Reconsider Prob. 5–179. Using EES (or other)software, investigate the effect of the inlet temperatureof cold water on the energy saved by using the lowflowshower head. Let the inlet temperature vary from 10°Cto 20°C. Plot the electric energy savings against the waterinlet temperature, and discuss the results.5–181 A fan is powered by a 0.5-hp motor and delivers airat a rate of 85 m 3 /min. Determine the highest value for theaverage velocity of air mobilized by the fan. Take the densityof air to be 1.18 kg/m 3 .5–182 An air-conditioning system requires airflow at themain supply duct at a rate of 180 m 3 /min. The average velocityof air in the circular duct is not to exceed 10 m/s to avoidexcessive vibration and pressure drops. Assuming the fanconverts 70 percent of the electrical energy it consumes intokinetic energy of air, determine the size of the electric motorneeded to drive the fan and the diameter of the main duct.Take the density of air to be 1.20 kg/m 3 .trapped in the bottle eventually reaches thermal equilibriumwith the atmosphere as a result of heat transfer through thewall of the bottle. The valve remains open during the processso that the trapped air also reaches mechanical equilibriumwith the atmosphere. Determine the net heat transfer throughthe wall of the bottle during this filling process in terms ofthe properties of the system and the surrounding atmosphere.5–184 An adiabatic air compressor is to be powered by adirect-coupled adiabatic steam turbine that is also driving agenerator. Steam enters the turbine at 12.5 MPa and 500°C ata rate of 25 kg/s and exits at 10 kPa and a quality of 0.92. Airenters the compressor at 98 kPa and 295 K at a rate of 10kg/s and exits at 1 MPa and 620 K. Determine the net powerdelivered to the generator by the turbine.Aircomp.98 kPa295 K1 MPa620 KFIGURE P5–18412.5 MPa500°CSteamturbine10 kPa5–185 Water flows through a shower head steadily at a rateof 10 L/min. An electric resistance heater placed in the waterpipe heats the water from 16 to 43°C. Taking the density ofwater to be 1 kg/L, determine the electric power input to theheater, in kW.In an effort to conserve energy, it is proposed to pass thedrained warm water at a temperature of 39°C through a heatexchanger to preheat the incoming cold water. If the heatexchanger has an effectiveness of 0.50 (that is, it recovers180 m 3 /min10 m/sResistanceheaterFIGURE P5–1825–183 Consider an evacuated rigid bottle of volume V thatis surrounded by the atmosphere at pressure P 0 and temperatureT 0 . A valve at the neck of the bottle is now opened andthe atmospheric air is allowed to flow into the bottle. The airFIGURE P5–185