Thermodynamics

272 | Thermodynamicsfind the simplest expression for the mixture temperature writtenin the formT 3 f a m# 1m # , m# 23 m # , T 1 , T 2 b3•m 1 , T 1•• Mixing device mm 2 , T 3 , T 32FIGURE P5–1605–161 An ideal gas expands in an adiabatic turbine from1200 K, 600 kPa to 700 K. Determine the turbine inlet volumeflow rate of the gas, in m 3 /s, required to produce turbinework output at the rate of 200 kW. The average values of thespecific heats for this gas over the temperature range are c p 1.13 kJ/kg · K and c v 0.83 kJ/kg · K. R 0.30 kJ/kg · K.5–162 Consider two identical buildings: one in Los Angeles,California, where the atmospheric pressure is 101 kPaand the other in Denver, Colorado, where the atmosphericpressure is 83 kPa. Both buildings are maintained at 21°C,and the infiltration rate for both buildings is 1.2 air changesper hour (ACH). That is, the entire air in the building isreplaced completely by the outdoor air 1.2 times per hour ona day when the outdoor temperature at both locations is10°C. Disregarding latent heat, determine the ratio of the heatlosses by infiltration at the two cities.5–163 The ventilating fan of the bathroom of a building hasa volume flow rate of 30 L/s and runs continuously. The12.2°CFan30 L/sbuilding is located in San Francisco, California, where theaverage winter temperature is 12.2°C, and is maintained at22°C at all times. The building is heated by electricity whoseunit cost is $0.09/kWh. Determine the amount and cost of theheat “vented out” per month in winter.5–164 Consider a large classroom on a hot summer daywith 150 students, each dissipating 60 W of sensible heat. Allthe lights, with 6.0 kW of rated power, are kept on. The roomhas no external walls, and thus heat gain through the wallsand the roof is negligible. Chilled air is available at 15°C,and the temperature of the return air is not to exceed 25°C.Determine the required flow rate of air, in kg/s, that needs tobe supplied to the room to keep the average temperature ofthe room constant. Answer: 1.49 kg/s5–165 Chickens with an average mass of 2.2 kg and averagespecific heat of 3.54 kJ/kg · °C are to be cooled bychilled water that enters a continuous-flow-type immersionchiller at 0.5°C. Chickens are dropped into the chiller at auniform temperature of 15°C at a rate of 500 chickens perhour and are cooled to an average temperature of 3°C beforethey are taken out. The chiller gains heat from the surroundingsat a rate of 200 kJ/h. Determine (a) the rate of heatremoval from the chickens, in kW, and (b) the mass flow rateof water, in kg/s, if the temperature rise of water is not toexceed 2°C.5–166 Repeat Prob. 5–165 assuming heat gain of the chilleris negligible.5–167 In a dairy plant, milk at 4°C is pasteurized continuouslyat 72°C at a rate of 12 L/s for 24 h a day and 365 daysa year. The milk is heated to the pasteurizing temperature byhot water heated in a natural-gas-fired boiler that has an efficiencyof 82 percent. The pasteurized milk is then cooled bycold water at 18°C before it is finally refrigerated back to4°C. To save energy and money, the plant installs a regeneratorthat has an effectiveness of 82 percent. If the cost of naturalgas is $1.10/therm (1 therm 105,500 kJ), determinehow much energy and money the regenerator will save thiscompany per year.Bathroom22°C72°C72°CHot milkHeat(Pasteurizingsection)RegeneratorFIGURE P5–1674°CColdmilkFIGURE P5–1635–168E A refrigeration system is being designed to cooleggs (r 67.4 lbm/ft 3 and c p 0.80 Btu/lbm · °F) with anaverage mass of 0.14 lbm from an initial temperature of 90°F