The window-mounted air conditioner shown in Fig. P10.24

Refrigerant 22 is the working fluid in a Carnot refrigeration cycle operating at steady state. The refrigerant enters the condenser as saturated vapor at \(32^{\circ} \mathrm{C}\) and exits as saturated liquid. The evaporator operates at \(0^{\circ} \mathrm{C}\). What is the coefficient of performance of the cycle? Determine, in kJ per kg of refrigerant flowing, (a) the work input to the compressor. (b) the work developed by the turbine. (c) the heat transfer to the refrigerant passing through the evaporator.

Refrigerant 22 is the working fluid in a Carnot vapor refrigeration cycle for which the evaporator temperature is -\(30^{\circ} \mathrm{C}\). Saturated vapor enters the condenser at \(36{\circ} \mathrm{C}\), and saturated liquid exits at the same temperature. The mass flow rate of refrigerant is 10 kg/min. Determine (a) the rate of heat transfer to the refrigerant passing through the evaporator, in kW. (b) the net power input to the cycle, in kW. (c) the coefficient of performance. (d) the refrigeration capacity, in tons.

A Carnot vapor refrigeration cycle operates between thermal reservoirs at \(4^{\circ} \mathrm{C}\) and \(30^{\circ} \mathrm{C}\). The working fluid is saturated vapor at the end of the compression process and saturated liquid at the beginning of the expansion process. For (a) Refrigerant 134a, (b) propane, (c) water, (d) ammonia, (e) \(\mathrm{CO}_{2}\) (using Fig. A-10), and (f) Refrigerant 410A (using Fig. A-11) as the working fluid, determine the operating pressures in the condenser and evaporator, in bar, and the coefficient of performance.

Consider a Carnot vapor refrigeration cycle with Refrigerant 134a as the working fluid. The cycle maintains a cold region at \(40^{\circ} \mathrm{F}\) when the ambient temperature is \(90^{\circ} \mathrm{F}\). Data at principal states in the cycle are given in the table below. The states are numbered as in Fig. 10.1. Sketch the T–s diagram for the cycle and determine the (a) temperatures in the evaporator and condenser, each in \({ }^{\circ} \mathrm{R}\). (b) compressor and turbine work, each in Btu per lb of refrigerant flowing. (c) coefficient of performance. (d) coefficient of performance for a Carnot cycle operating at the reservoir temperatures. Compare the coefficients of performance determined in (c) and (d), and comment.

For the cycle in Problem 10.4, determine (a) the rates of heat transfer, in Btu per lb of refrigerant flowing, for the refrigerant flowing through the evaporator and condenser, respectively. (b) the rates and directions of exergy transfer accompanying each of these heat transfers, in Btu per lb of refrigerant flowing. Let \(T_{0}=90^{\circ} \mathrm{F}\).

An ideal vapor-compression refrigeration cycle operates at steady state with Refrigerant 134a as the working fluid. Saturated vapor enters the compressor at 2 bar, and saturated liquid exits the condenser at 8 bar. The mass flow rate of refrigerant is 7 kg/min. Determine (a) the compressor power, in kW. (b) the refrigerating capacity, in tons. (c) the coefficient of performance.

Plot each of the quantities in Problem 10.6 versus evaporator temperature for evaporator pressures ranging from 0.6 to 4 bar, while the condenser pressure remains fixed at 8 bar.

Refrigerant 134a is the working fluid in an ideal vapor- compression refrigeration cycle operating at steady state. Refrigerant enters the compressor at 1.4 bar, - \(12^{\circ} \mathrm{C}\), and the condenser pressure is 9 bar. Liquid exits the condenser at \(32^{\circ} \mathrm{C}\). The mass flow rate of refrigerant is 7 kg/min. Determine (a) the compressor power, in kW. (b) the refrigeration capacity, in tons. (c) the coefficient of performance.

Figure P10.9 provides steady-state operating data for an ideal vapor-compression refrigeration cycle with Refrigerant 134a as the working fluid. The mass flow rate of refrigerant is 30.59 lb/min. Sketch the T–s diagram for the cycle and determine (a) the compressor power, in horsepower. (b) the rate of heat transfer, from the working fluid passing through the condenser, in Btu/min. (c) the coefficient of performance.

Refrigerant 22 enters the compressor of an ideal vapor- compression refrigeration system as saturated vapor at -\(40^{\circ} \mathrm{C}\) with a volumetric flow rate of \(15 \mathrm{~m}^{3} / \mathrm{min}\). The refrigerant leaves the condenser at \(19^{\circ} \mathrm{C}\), 9 bar. Determine (a) the compressor power, in kW. (b) the refrigerating capacity, in tons. (c) the coefficient of performance. (d) the rate of entropy production for the cycle, in kW/K.

Ammonia with a mass flow rate of 5 kg/min is the working fluid within an ideal vapor-compression refrigeration cycle. Saturated vapor enters the compressor and saturated liquid exits the condenser. The evaporator temperature is \(-10^{\circ} \mathrm{C}\) and the condenser pressure is 10 bar. Determine (a) the coefficient of performance. (b) the refrigerating capacity, in tons.

Refrigerant 134a enters the compressor of an ideal vapor-compression refrigeration cycle as saturated vapor at \(-10^{\circ} \mathrm{F}\) . The condenser pressure is \(160 \mathrm{lbf} / \mathrm{in} .{ }^{2}\) The mass flow rate of refrigerant is 6 lb/min. Plot the coefficient of performance and the refrigerating capacity, in tons, versus the condenser exit temperature ranging from the saturation temperature at \(160 \mathrm{lbf} / \mathrm{in}^{2} \text { to } 90^{\circ} \mathrm{F}\).

An ideal vapor-compression refrigeration cycle with ammonia as the working fluid has an evaporator temperature of \(-20^{\circ} \mathrm{C}\) and a condenser pressure of 12 bar. Saturated vapor enters the compressor and saturated liquid exits the condenser. The mass flow rate of the refrigerant is 3 kg/min. Determine (a) the coefficient of performance. (b) the refrigerating capacity, in tons. To determine the effect of changing the evaporator temperature on the cycle performance, plot the coefficient of performance and the refrigerating capacity, in tons, for saturated vapor entering the compressor at temperatures ranging from \(-40^{\circ} \mathrm{C}\) to \(-10^{\circ} \mathrm{C}\)

To determine the effect of changing condenser pressure on the performance of an ideal vapor-compression refrigeration cycle, plot the coefficient of performance and the refrigerating capacity, in tons, for the cycle in Problem 10.13 for condenser pressures ranging from 8 to 16 bar. All other conditions are the same as in Problem 10.13.

A vapor-compression refrigeration cycle operates at steady state with Refrigerant 134a as the working fluid. Saturated vapor enters the compressor at 2 bar, and saturated liquid exits the condenser at 8 bar. The isentropic compressor efficiency is 80%. The mass flow rate of refrigerant is 7 kg/min. Determine (a) the compressor power, in kW. (b) the refrigeration capacity, in tons. (c) the coefficient of performance.

Modify the cycle in Problem 10.9 to have an isentropic compressor efficiency of 83% and let the temperature of the liquid leaving the condenser be \(100^{\circ} \mathrm{F}\). Determine, for the modified cycle, (a) the compressor power, in horsepower. (b) the rate of heat transfer from the working fluid passing through the condenser, in Btu/min. (c) the coefficient of performance. (d) the rates of entropy production in the compressor and expansion valve, in \(\mathrm{Btu} / \mathrm{min} \cdot{ }^{\circ} \mathrm{R}\). (e) the rates of exergy destruction in the compressor and expansion valve, each in Btu/min. Let \(T_{0}=90^{\circ} \mathrm{F}\).

Data for steady-state operation of a vapor-compression refrigeration cycle with Refrigerant 134a as the working fluid are given in the table below. The states are numbered as in Fig. 10.3. The refrigeration capacity is 4.6 tons. Ignoring heat transfer between the compressor and its surroundings, sketch the T–s diagram of the cycle and determine (a) the mass flow rate of the refrigerant, in kg/min. (b) the isentropic compressor efficiency. (c) the coefficient of performance. (d) the rates of exergy destruction in the compressor and expansion valve, each in kW. (e) the net changes in flow exergy rate of the refrigerant passing through the evaporator and condenser, respectively, each in kW. \(\text { Let } T_{0}=21^{\circ} \mathrm{C}, p_{0}=1 \mathrm{bar} \text {. }\)

A vapor-compression refrigeration system uses ammonia as the working fluid. Data for the cycle are provided in the table below. The principal states are numbered as in Fig. 10.3. The heat transfer rate from the working fluid passing through the condenser is 50,000 Btu/h. If the compressor operates adiabatically, determine (a) the compressor power input, in hp. (b) the coefficient of performance of the cycle.

If the minimum and maximum allowed refrigerant pressures are 1 and 10 bar, respectively, which of the following can be used as the working fluid in a vapor-compression refrigeration system that maintains a cold region at \(0^{\circ} \mathrm{C}\), while discharging energy by heat transfer to the \(30^{\circ} \mathrm{C}\): Refrigerant 22, Refrigerant 134a, ammonia, propane?

Consider the following vapor-compression refrigeration cycle used to maintain a cold region at temperature \(??T_{\mathrm{C}}\) when the ambient temperature is \(80^{\circ} \mathrm{F}\): Saturated vapor enters the compressor at \(18^{\circ} \mathrm{F}\) below TC, and the compressor operates adiabatically with an isentropic efficiency of 80%. Saturated liquid exits the condenser at \(95^{\circ} \mathrm{F}\). There are no pressure drops through the evaporator or condenser, and the refrigerating capacity is 1 ton. Plot refrigerant mass flow rate, in lb/min, coefficient of performance, and refrigerating efficiency, versus \(??T_{\mathrm{C}}\) ranging from \(40^{\circ} \mathrm{F}\) to \(-25^{\circ} \mathrm{F}\) if the refrigerant is (a) Refrigerant 134a. (b) propane. (c) Refrigerant 22. (d) ammonia. The refrigerating efficiency is defined as the ratio of the cycle coefficient of performance to the coefficient of performance of a Carnot refrigeration cycle operating between thermal reservoirs at the ambient temperature and the temperature of the cold region.

In a vapor-compression refrigeration cycle, ammonia exits the evaporator as saturated vapor at \(-22^{\circ} \mathrm{C}\) . The refrigerant enters the condenser at 16 bar and 1\(160^{\circ} \mathrm{C}\) , and saturated liquid exits at 16 bar. There is no significant heat transfer between the compressor and its surroundings, and the refrigerant passes through the evaporator with a negligible change in pressure. If the refrigerating capacity is 150 kW, determine (a) the mass flow rate of the refrigerant, in kg/s. (b) the power input to the compressor, in kW. (c) the coefficient of performance. (d) the isentropic compressor efficiency. (e) the rate of entropy production, in kW/K, for the compressor.

A vapor-compression refrigeration system with a capacity of 10 tons has Refrigerant 134a as the working fluid. Information and data for the cycle are provided in Fig. P10.22 and in the table below. The compression process is internally reversible and can be modeled by \(p v^{1.01}=\text { constant }\). The condenser is water-cooled, with water entering and leaving with a negligible change in pressure. Heat transfer from the outside of the condenser can be neglected. Determine (a) the mass flow rate of refrigerant, in kg/s. (b) the power input and the heat transfer rate for the compressor, each in kW. (c) the coefficient of performance. (d) the mass flow rate of the cooling water, in kg/s. (e) the rates of entropy production in the condenser and expansion valve, in kW/K. (f) the rates of exergy destruction in the condenser and expansion valve, each expressed as a percentage of the compressor power input. Let \(T_{0}=20^{\circ} \mathrm{C}\).

Data for steady-state operation of a vapor-compression refrigeration cycle with propane as the working fluid are given in the table below. The states are numbered as in Fig. 10.3. The mass flow rate of refrigerant is 8.42 lb/min. Heat transfer from the compressor to its surroundings occurs at a rate of 3.5 Btu per lb of refrigerant passing through the compressor. The condenser is water-cooled, with water entering at \(65^{\circ} \mathrm{F}\) and leaving at \(80^{\circ} \mathrm{F}\) with negligible change in pressure. Sketch the T–s diagram of the cycle and determine (a) the refrigeration capacity, in tons. (b) the compressor power, in horsepower. (c) the mass flow rate of the condenser cooling water, in lb/min. (d) the coefficient of performance.

The window-mounted air conditioner shown Fig.P10.24 supplies \(19 \mathrm{~m}^{3} / \mathrm{min} \text { of air at } 15^{\circ} \mathrm{C}\), 1 bar to a room. Air returns from the room to the evaporator of the unit at \(22^{\circ} \mathrm{C}\) . The air conditioner operates at steady state on a vapor-compression refrigeration cycle with Refrigerant 22 entering the compressor at 4 bar, \(10^{\circ} \mathrm{C}\) . Saturated liquid refrigerant at 9 bar leaves the condenser. The compressor has an isentropic efficiency of 70%, and refrigerant exits the compressor at 9 bar. Determine the compressor power, in kW, the refrigeration capacity, in tons, and the coefficient of performance.

A vapor-compression refrigeration system for household refrigerator has a refrigerating capacity of 900 Btu/h. Refrigerant enters the evaporator at \(-15^{\circ} \mathrm{F}\) and exits at \(20^{\circ} \mathrm{F}\). The isentropic compressor efficiency is 75%. The refrigerant condenses at \(110^{\circ} \mathrm{F}\) and exits the condenser subcooled at \(100^{\circ} \mathrm{F}\) . There are no significant pressure drops in the flows through the evaporator and condenser. Determine the evaporator and condenser pressures, each in \(\text { lbf/in. }{ }^{2}\), the mass flow rate of refrigerant, in lb/min, the compressor power input, in horsepower, and the coefficient of performance for working fluids: (a) Refrigerant 134a, (b) propane, (c) \(\mathrm{CO}_{2}\) (using data from Fig. A-10E).

A vapor-compression air-conditioning system operates at steady state as shown in Fig. P10.26. The system maintains a cool region at \(60^{\circ} \mathrm{F}\) and discharges energy by heat transfer to the surroundings at 908F. Refrigerant 134a enters the compressor as a saturated vapor at \(40^{\circ} \mathrm{F}\) and is compressed adiabatically to 160 lbf/in.2 The isentropic compressor efficiency is 80%. Refrigerant exits the condenser as a saturated liquid at \(160 \mathrm{lbf} / \mathrm{in}^{2}\) The mass flow rate of the refrigerant is 0.15 lb/s. Kinetic and potential energy changes are negligible as are changes in pressure for flow through the evaporator and condenser. Determine (a) the power required by the compressor, in Btu/s. (b) the coefficient of performance. (c) the rates of exergy destruction in the compressor and expansion valve, each in Btu/s. (d) the rates of exergy destruction and exergy transfer accompanying heat transfer, each in Btu/s, for a control volume comprising the evaporator and a portion of the cool region such that heat transfer takes place at \(T_{\mathrm{C}}=520^{\circ} \mathrm{R}\) ( \(60^{\circ} \mathrm{F}\) ). (e) the rates of exergy destruction and exergy transfer accompanying heat transfer, each in Btu/s, for a control volume enclosing the condenser and a portion of the surroundings such that heat transfer takes place at \(T_{\mathrm{H}}=550^{\circ} \mathrm{R}\) ( \(90^{\circ} \mathrm{F}\) ). Let \(T_{\mathrm{0}}=550^{\circ} \mathrm{R}\)

A vapor-compression refrigeration cycle with Refrigerant 134a as the working fluid operates with an evaporator temperature of \(50^{\circ} \mathrm{F}\) and a condenser pressure of \(180 \mathrm{lbf} / \mathrm{in}^{2}\) Saturated vapor enters the compressor. Refrigerant enters the condenser at \(140^{\circ} \mathrm{F}\) and exits as saturated liquid. The cycle has a refrigeration capacity of 5 tons. Determine (a) the refrigerant mass flow rate, in lb/min. (b) the compressor isentropic efficiency. (c) the compressor power, in horsepower. (d) the coefficient of performance. Plot each of the quantities calculated in parts (b) through (d) for compressor exit temperatures varying from \(130^{\circ} \mathrm{F}\) to \(140^{\circ} \mathrm{F}\).

A vapor-compression refrigeration system operates with the cascade arrangement of Fig. 10.9. Refrigerant 22 is the working fluid in the high-temperature cycle and Refrigerant 134a is used in the low-temperature cycle. For the Refrigerant 134a cycle, the working fluid enters the compressor as saturated vapor at \(-30^{\circ} \mathrm{F}\) and is compressed isentropically to \(50 \mathrm{lbf} / \mathrm{in}^{2}\) Saturated liquid leaves the intermediate heat exchanger at \(50 \mathrm{lbf} / \mathrm{in}^{2}\) and enters the expansion valve. For the Refrigerant 22 cycle, the working fluid enters the compressor as saturated vapor at a temperature \(5^{\circ} \mathrm{F}\) below that of the condensing temperature of the Refrigerant 134a in the intermediate heat exchanger. The Refrigerant 22 is compressed isentropically to \(250 \mathrm{lbf} / \mathrm{in}^{2}\) Saturated liquid then enters the expansion valve at \(250 \mathrm{lbf} / \mathrm{in}^{2}\) The refrigerating capacity of the cascade system is 20 tons. Determine (a) the power input to each compressor, in Btu/min. (b) the overall coefficient of performance of the cascade cycle. (c) the rate of exergy destruction in the intermediate heat exchanger, in Btu/min. Let \(\text { Let } T_{0}=80^{\circ} \mathrm{F}, p_{0}=14.7 \mathrm{lbf} / \mathrm{in}^{2}\)

A vapor-compression refrigeration system uses the arrangement shown in Fig. 10.10 for two-stage compression with intercooling between the stages. Refrigerant 134a is the working fluid. Saturated vapor at \(-30^{\circ} \mathrm{C}\) enters the first compressor stage. The flash chamber and direct contact heat exchanger operate at 4 bar, and the condenser pressure is 12 bar. Saturated liquid streams at 12 and 4 bar enter the high- and low-pressure expansion valves, respectively. If each compressor operates isentropically and the refrigerating capacity of the system is 10 tons, determine (a) the power input to each compressor, in kW. (b) the coefficient of performance.

Figure P10.30 shows a two-stage vapor-compression refrigeration system with ammonia as the working fluid. The system uses a direct-contact heat exchanger to achieve intercooling. The evaporator has a refrigerating capacity of 30 tons and produces \(-20^{\circ} \mathrm{F}\) saturated vapor at its exit. In the first compressor stage, the refrigerant is compressed adiabatically to \(80 \mathrm{lbf} / \mathrm{in} .^{2}\), which is the pressure in the direct contact heat exchanger. Saturated vapor at \(80 \mathrm{lbf} / \mathrm{in} .^{2}\) enters the second compressor stage and is compressed adiabatically to \(250 \mathrm{lbf} / \mathrm{in} .^{2}\) Each compressor stage has an isentropic efficiency of 85%. There are no significant pressure drops as the refrigerant passes through the heat exchangers. Saturated liquid enters each expansion valve. Determine (a) the ratio of mass flow rates, \(\dot{m}_{3} / \dot{m}_{1}\). (b) the power input to each compressor stage, in horsepower. (c) the coefficient of performance. (d) Plot each of the quantities calculated in parts (a)–(c) versus the direct-contact heat exchanger pressure ranging from 20 to \(200 \mathrm{lbf} / \mathrm{in} .^{2}\) Discuss.

Figure P10.31 shows a two-stage, vapor-compression refrigeration system with two evaporators and a direct contact heat exchanger. Saturated vapor ammonia from evaporator 1 enters compressor 1 at \(18 \mathrm{lbf} / \mathrm{in}^{2}\) and exits at \(70 \mathrm{lbf} / \mathrm{in} .^{2}\). Evaporator 2 operates at \(70 \mathrm{lbf} / \mathrm{in} .^{2}\) , with saturated vapor exiting at state 8. The condenser pressure is \(200 \mathrm{lbf} / \mathrm{in}^{2}\), and saturated liquid refrigerant exits the condenser. Each compressor stage has an isentropic efficiency of 80%. The refrigeration capacity of each evaporator is shown on the figure. Sketch the T–s diagram of the cycle and determine (a) the temperatures, in \({ }^{\circ} \mathrm{F}\), of the refrigerant in each evaporator. (b) the power input to each compressor stage, in horsepower. (c) the overall coefficient of performance.

Figure P10.32 shows the schematic diagram of a vapor- compression refrigeration system with two evaporators using Refrigerant 134a as the working fluid. This arrangement is used to achieve refrigeration at two different temperatures with a single compressor and a single condenser. The lower- temperature evaporator has a refrigerating capacity of 3 tons while the higher-temperature evaporator has a refrigerating capacity of 2 tons. Operating data are provided in the accompanying table. Calculate (a) the mass flow rate of refrigerant through each evaporator, in kg/min. (b) the compressor power input, in kW. (c) the rate of heat transfer from the refrigerant passing through the condenser, in kW.

An ideal vapor-compression refrigeration cycle modified to include a counterflow heat exchanger, as shown in Fig. P10.33. Ammonia leaves the evaporator as saturated vapor at 1.0 bar and is heated at constant pressure to \(5^{\circ} \mathrm{C}\) before entering the compressor. Following isentropic compression to 18 bar, the refrigerant passes through the condenser, exiting at \(40^{\circ} \mathrm{C}\), 18 bar. The liquid then passes through the heat exchanger, entering the expansion valve at 18 bar. If the mass flow rate of refrigerant is 12 kg/min, determine (a) the refrigeration capacity, in tons of refrigeration. (b) the compressor power input, in kW. (c) the coefficient of performance. (d) the rate of entropy production in the compressor, in kW/K. (e) the rate of exergy destruction in the compressor, in kW. Let \(T_{0}=20^{\circ} \mathrm{C}\) Discuss advantages and disadvantages of this arrangement.

Figure P10.34 gives data for an ideal vapor-compression heat pump cycle operating at steady state with Refrigerant 134a as the working fluid. The heat pump provides heating at a rate of 15 kW to maintain the interior of a building at \(20^{\circ} \mathrm{C}\) when the outside temperature is \(5^{\circ} \mathrm{C}\). Sketch the T–s diagram for the cycle and determine the (a) temperatures at the principal states of the cycle, each in \({ }^{\circ} \mathrm{C}\). (b) power input to the compressor, in kW. (c) coefficient of performance. (d) coefficient of performance for a Carnot heat pump cycle operating between reservoirs at the building interior and outside temperatures, respectively. Compare the coefficients of performance determined in (c) and (d). Discuss.

Refrigerant 134a is the working fluid in a vapor compression heat pump system with a heating capacity of 70,000 Btu/h. The condenser operates at \(180 \mathrm{lbf} / \mathrm{in}^{2}\), and the evaporator temperature is \(20^{\circ} \mathrm{F}\). The refrigerant is a saturated vapor at the evaporator exit and exits the condenser at \(120^{\circ} \mathrm{F}\). Pressure drops in the flows through the evaporator and condenser are negligible. The compression process is adiabatic, and the temperature at the compressor exit is \(200^{\circ} \mathrm{F}\). Determine (a) the mass flow rate of refrigerant, in lb/min. (b) the compressor power input, in horsepower. (c) the isentropic compressor efficiency. (d) the coefficient of performance.

Refrigerant 134a is the working fluid in a vapor- compression heat pump that provides 35 kW to heat a dwelling on a day when the outside temperature is below freezing. Saturated vapor enters the compressor at 1.6 bar, and saturated liquid exits the condenser, which operates at 8 bar. Determine for isentropic compression (a) the refrigerant mass flow rate, in kg/s. (b) the compressor power, in kW. (c) the coefficient of performance. Recalculate the quantities in parts (b) and (c) for an isentropic compressor efficiency of 75%.

An office building requires a heat transfer rate of 20 kW to maintain the inside temperature at \(21^{\circ} \mathrm{C}\) when the outside temperature is \(0^{\circ} \mathrm{C}\). A vapor-compression heat pump with Refrigerant 134a as the working fluid is to be used to provide the necessary heating. The compressor operates adiabatically with an isentropic efficiency of 82%. Specify appropriate evaporator and condenser pressures of a cycle for this purpose assuming \(\Delta T_{\text {cond }}=\Delta T_{\text {evap }}=10^{\circ} \mathrm{C}\), as shown in Figure P10.37. The states are numbered as in Fig. 10.13. The refrigerant exits the evaporator as saturated vapor and exits the condenser as saturated liquid at the respective pressures. Determine the (a) mass flow rate of refrigerant, in kg/s. (b) compressor power, in kW. (c) coefficient of performance and compare with the coefficient of performance for a Carnot heat pump cycle operating between reservoirs at the inside and outside temperatures, respectively.

Repeat the calculations of Problem 10.37 for Refrigerant 22 as the working fluid. Compare the results with those of Problem 10.37 and discuss.

A process requires a heat transfer rate of \(3 \times 10^{6} \mathrm{Btu} / \mathrm{h}\) at \(170^{\circ} \mathrm{F}\). It is proposed that a Refrigerant 134a vapor- compression heat pump be used to develop the process heating using a wastewater stream at \(125^{\circ} \mathrm{F}\) as the lower- temperature source. Figure P10.39 provides data for this cycle operating at steady state. The compressor isentropic efficiency is 80%. Sketch the T–s diagram for the cycle and determine the (a) specific enthalpy at the compressor exit, in Btu/lb. (b) temperatures at each of the principal states, in \({ }^{\circ} \mathrm{F}\). (c) mass flow rate of the refrigerant, in lb/h. (d) compressor power, in Btu/h. (e) coefficient of performance and compare with the coefficient of performance for a Carnot heat pump cycle operating between reservoirs at the process temperature and the wastewater temperature, respectively.

A vapor-compression heat pump has a heating capacity of 500 kJ/min and uses Refrigerant 134a as the working fluid. The isentropic compressor efficiency is 80%. The heat pump is driven by a power cycle with a thermal efficiency of 25%. For the power cycle, 80% of the heat rejected is transferred to the heated space. Data for the cycle are provided in the table below. The principal states are numbered as in Fig. 10.3. (a) Determine the power input to the heat pump compressor, in kW. (b) Evaluate the ratio of the total rate that heat is delivered to the heated space to the rate of heat input to the power cycle. Discuss.

Refrigerant 134a enters the compressor of a vapor compression heat pump at \(15 \mathrm{lbf} / \mathrm{in} .^{2}, 0^{\circ} \mathrm{F}\) and is compressed adiabatically to \(160 \mathrm{lbf} / \mathrm{in}^{2}, 160^{\circ} \mathrm{F}\). Liquid enters the expansion valve at \(160 \text { lbf/in. }{ }^{2}, 95^{\circ} \mathrm{F}\). At the valve exit, the pressure is \(15 \mathrm{lbf} / \mathrm{in}^{2}\) (a) Determine the isentropic compressor efficiency. (b) Determine the coefficient of performance. (c) Perform a full exergy accounting of the compressor power input, in Btu per lb of refrigerant flowing. Discuss. Let \(T_{0}=480^{\circ} \mathrm{R}\)

A geothermal heat pump operating at steady state with Refrigerant-22 as the working fluid is shown schematically in Fig. P10.42. The heat pump uses \(55^{\circ} \mathrm{F}\) water from wells as the thermal source. Operating data are shown on the figure for a day in which the outside air temperature is \(20^{\circ} \mathrm{F}\). Assume adiabatic operation of the compressor. For the heat pump, determine a) the volumetric flow rate of heated air to the house, in \(\mathrm{ft}^{3} / \mathrm{min} .\). (b) the isentropic compressor efficiency. (c) the compressor power, in horsepower. (d) the coefficient of performance. (e) the volumetric flow rate of water from the geothermal wells, in gal/min. For \(T_{0}=20^{\circ} \mathrm{F}\), perform a full exergy accounting of the compressor power input, and devise and evaluate a second law efficiency for the heat pump system.

Air enters the compressor of an ideal Brayton refrigeration cycle at 100 kPa, 300 K. The compressor pressure ratio is 3.75, and the temperature at the turbine inlet is 350 K. Determine the (a) net work input, per unit mass of air flow, in kJ/kg. (b) refrigeration capacity, per unit mass of air flow, in kJ/kg. (c) coefficient of performance. (d) coefficient of performance of a Carnot refrigeration cycle operating between thermal reservoirs at \(T_{\mathrm{C}}=300 \mathrm{~K}\) and \(T_{\mathrm{H}}=300 \mathrm{~K}\), respectively.

Air enters the compressor of a Brayton refrigeration cycle at 100 kPa, 270 K. The compressor pressure ratio is 3, and the temperature at the turbine inlet is 315 K. The compressor and turbine have isentropic efficiencies of 82% and 85%, respectively. Determine the (a) net work input, per unit mass of air flow, in kJ/kg. (b) exergy accounting of the net power input, in kJ per kg of air flowing. Discuss. Let \(T_{\mathrm{0}}=315 \mathrm{~K}\).

Plot the quantities calculated in parts (a) through (c) of Problem 10.43 versus the compressor pressure ratio ranging from 3 to 6. Repeat for compressor and turbine isentropic efficiencies of 90%, 85%, and 80%.

An ideal Brayton refrigeration cycle has a compressor pressure ratio of 7. At the compressor inlet, the pressure and temperature of the entering air are \(22 \mathrm{lbf} / \mathrm{in} .^{2} \text { and } 450^{\circ} \mathrm{R}\), respectively. The temperature at the inlet of the turbine is 6808R. For a refrigerating capacity of 13.5 tons, determine (a) the mass flow rate of the refrigerant, in lb/min. (b) the net power input, in Btu/min. (c) the coefficient of performance.

Reconsider Problem 10.46, but include in the analysis that the compressor and turbine have isentropic efficiencies of 75% and 89%, respectively. Answer the same questions as in Problem 10.46 and determine the rate of entropy production within the compressor and turbine, each in \(\text { Btu/min } \cdot{ }^{\circ} \mathrm{R}\).

The table below provides steady-state operating data for an ideal Brayton refrigeration cycle with air as the working fluid. The principal states are numbered as in Fig. 10.15. The volumetric flow rate at the turbine inlet is \(0.4 \mathrm{~m}^{3} / \mathrm{s}\). Sketch the T–s diagram for the cycle and determine the (a) specific enthalpy, in kJ/kg, at the turbine exit. (b) mass flow rate, in kg/s. (c) net power input, in kW. (d) refrigeration capacity, in kW. (e) coefficient of performance.

Air enters the compressor of a Brayton refrigeration cycle at 100 kPa, 260 K, and is compressed adiabatically to 300 kPa. Air enters the turbine at 300 kPa, 300 K, and expands adiabatically to 100 kPa. For the cycle (a) determine the net work per unit mass of air flow, in kJ/kg, and the coefficient of performance if the compressor and turbine isentropic efficiencies are both 100%. (b) plot the net work per unit mass of air flow, in kJ/kg, and the coefficient of performance for equal compressor and turbine isentropic efficiencies ranging from 80 to 100%.

The Brayton refrigeration cycle of Problem 10.43 is modified by the introduction of a regenerative heat exchanger. In the modified cycle, compressed air enters the regenerative heat exchanger at 350 K and is cooled to 320 K before entering the turbine. Determine, for the modified cycle, (a) the lowest temperature, in K. (b) the net work input per unit mass of air flow, in kJ/kg. (c) the refrigeration capacity, per unit mass of air flow, in kJ/kg. (d) the coefficient of performance.

Reconsider Problem 10.50, but include in the analysis that the compressor and turbine have isentropic efficiencies of 85 and 88% respectively. Answer the same questions as in Problem 10.50.

Plot the quantities calculated in parts (a) through (d) of Problem 10.50 versus the compressor pressure ratio ranging from 4 to 7. Repeat for equal compressor and turbine isentropic efficiencies of 95%, 90%, and 80%.

Consider a Brayton refrigeration cycle with a regenerative heat exchanger. Air enters the compressor at \(500^{\circ} \mathrm{R}, 16 \mathrm{lbf} / \mathrm{in} .^{2}\) and is compressed isentropically to \(45 \text { lbf/in. }{ }^{2}\) Compressed air enters the regenerative heat exchanger at \(550^{\circ} \mathrm{R}\) and is cooled to \(490^{\circ} \mathrm{R}\) before entering the turbine. The expansion through the turbine is isentropic. If the refrigeration capacity is 14 tons, calculate (a) the volumetric flow rate at the compressor inlet, in ft3/min. (b) the coefficient of performance.

Reconsider Problem 10.53, but include in the analysis that the compressor and turbine each have isentropic efficiencies of 84%. Answer the same questions for the modified cycle in Problem 10.53 and determine the rate of entropy production within the compressor and turbine, each in \(\text { Btu } / \text { min }{ }^{\circ} \mathrm{R} \text {. }\)

Air at 2.5 bar, 400 K is extracted from a main jet engine compressor for cabin cooling. The extracted air enters a heat exchanger where it is cooled at constant pressure to 325 K through heat transfer with the ambient. It then expands adiabatically to 1.0 bar through a turbine and is discharged into the cabin. The turbine has an isentropic efficiency of 80%. If the mass flow rate of the air is 2.0 kg/s, determine (a) the power developed by the turbine, in kW. (b) the rate of heat transfer from the air to the ambient, in kW.

Air at \(30 \mathrm{lbf} / \mathrm{in} .^{2}, 700^{\circ} \mathrm{R}\) is extracted from a main jet engine compressor for cabin cooling. The extracted air enters a heat exchanger where it is cooled at constant pressure to \(520^{\circ} \mathrm{R}\) through heat transfer with the ambient. It then expands adiabatically to \(15 \text { lbf/in. }{ }^{2}\) through a turbine and is discharged into the cabin at \(520^{\circ} \mathrm{R}\) with a mass flow rate of 220 lb/min. Determine (a) the power developed by the turbine, in horsepower. (b) the isentropic turbine efficiency.

Air within a piston–cylinder assembly undergoes a Stirling refrigeration cycle, which is the reverse of the Stirling power cycle introduced in Sec. 9.8.4. At the beginning of the isothermal compression, the pressure and temperature are 100 kPa and 350 K, respectively. The compression ratio is 7, and the temperature during the isothermal expansion is 150 K. Determine the (a) heat transfer for the isothermal compression, in kJ per kg of air. (b) net work for the cycle, in kJ per kg of air. (c) coefficient of performance.

Air undergoes an Ericsson refrigeration cycle, which is the reverse of the Ericsson power cycle introduced in Sec. 9.8.4. Figure P10.58 provides data for the cycle operating at steady state. Sketch the p–v diagram for the cycle and determine the (a) heat transfer for the isothermal expansion, per unit mass of air flow, in kJ/kg. (b) net work, per unit mass of air flow, in kJ/kg. (c) coefficient of performance.

Children may wonder how a household refrigerator works to keep food cold in a warm kitchen. Prepare a 20-minute presentation suitable for an elementary school science class to explain the principles of operation of a refrigerator. Include instructional aids to enhance your presentation.

The object of this project is to select a compact thermoelectric refrigerator to be shared by you and at least two other students living in the same residence as you do. Survey the other students to determine their needs in order to size the unit. Critically evaluate competing brands. What type and number of thermoelectric modules are used in the unit selected, and what is its power requirement? Summarize your findings in a memorandum.

In cases involving cardiac arrest, stroke, heart attack, and hyperthermia, hospital medical staff must move quickly to reduce the patient’s body temperature by several degrees. A system for this purpose featuring a disposable plastic body suit is described in BIOCONNECTIONS in Sec. 4.9. Conduct a search of the patent literature for alternative ways to achieve cooling of medically distressed individuals. Consider patents both granted and pending. Critically evaluate two different methods found in your search relative to each other and the body suit approach. Write a report including at least three references.

Identify and visit a local facility that uses cold thermal storage. Conduct a forensic study to determine if the cold storage system is well suited for the given application today. Consider costs, effectiveness in providing the desired cooling, contribution to global climate change, and other pertinent issues. Document the cold storage systems suitability for the application. If the cold storage system is not well suited, recommend system upgrades or an alternative approach for obtaining the desired cooling. Prepare a PowerPoint presentation of your findings.

Refrigerant 134a is widely used as the working fluid in air conditioners and refrigerators. However, its use will likely be phased out in the future due to concerns about its Global Warming Potential (GWP). Investigate which environmentally acceptable working fluids are under consideration to replace R-134a for these uses in the United States and internationally. Determine the design issues for air conditioners and refrigerators that would result from changing refrigerants. Create an executive summary of your findings with an accompanying appendix including your background research.

A horizontal, closed-loop geothermal heat pump system is under consideration for a residential development of 100 single-family homes, \(2000 \mathrm{ft}^{2}\) each. The local water table is 50 ft, and the groundwater temperature is \(56 \mathrm{ft}^{2}\). Develop preliminary specifications for a ground-source heat pump system having a run-around loop that provides geothermal water for the 100 homes in the development. Include specifications for the system’s accompanying trench design.

Food poisoning is on the rise and can be fatal. Many of those affected have eaten recently at a restaurant, café, or fast-food outlet serving food that has not been cooled properly by the food supplier or restaurant food-handlers. To be safe, foods should not be allowed to remain in the temperature range where bacteria most quickly multiply. Standard refrigerators typically do not have the ability to provide the rapid cooling needed to ensure dangerous levels of bacteria are not attained. A food processing company supplying a wide range of fish products to restaurants has requested your project group to provide advice on how to achieve best cooling practices in its factory. In particular, you are asked to consider applicable health regulations, suitable equipment, typical operating costs, and other pertinent issues. A written report providing your recommendations is required, including an annotated list of food-cooling Dos and Don’ts for restaurants supplied by the company with fish.

According to researchers, advances in nanomaterial fabrication are leading to development of tiny thermoelectric modules that could be used in various applications, including integrating nanoscale cooling devices within the uniforms of firefighters, emergency workers, and military personnel; embedding thermoelectric modules in facades of a building; and using thermoelectric modules to recover waste heat in automobiles. Research two applications for this technology proposed within the past five years. Investigate the technical readiness and economic feasibility for each concept. Report your findings in an executive summary and a PowerPoint presentation with at least three references.

EcoCute is a transcritical \(\mathrm{CO}_{2}\) heat pump used extensively in Europe and Japan. Investigate this technology and compare its operational schematic and accompanying T–s diagram with that shown in Fig. 10.18. Explore why this technology is not readily available and used within the United States. Compare its use for a \(1000 \mathrm{ft}^{2}\) dwelling in your locale with a more conventional air-cooled residential heat pump using a synthetic refrigerant in terms of costs (operational and initial) and environmental impact. What are the impediments to its deployment in the United States? Create a PowerPoint presentation of your findings and a supporting project report.

A vapor-compression refrigeration system operating continuously is being considered to provide a minimum of 80 tons of refrigeration for an industrial refrigerator maintaining a space at \(2^{\circ} \mathrm{C}\). The surroundings to which the system rejects energy by heat transfer reach a maximum temperature of \(40^{\circ} \mathrm{C}\). For effective heat transfer, the system requires a temperature difference of at least \(20^{\circ} \mathrm{C}\) between the condensing refrigerant and surroundings and between the vaporizing refrigerant and refrigerated space. The project manager wishes to install a system that minimizes the annual cost for electricity (monthly electricity cost is fixed at 5.692 cents for the first \(250 \mathrm{~kW} \cdot \mathrm{h}\) and 6.006 cents for any usage above \(250 \mathrm{~kW} \cdot \mathrm{h}\)). You are asked to evaluate two alternative designs: a standard vapor-compression refrigeration cycle and a vapor-compression refrigeration cycle that employs a power-recovery turbine in lieu of an expansion valve. For each alternative, consider three refrigerants: ammonia, Refrigerant 22, and Refrigerant 134a. Based on electricity cost, recommend the better choice between the two alternatives and a suitable refrigerant. Other than electricity cost, what additional factors should the manager consider in making a final selection? Prepare a written report including results, conclusions, and recommendations.

High-performance aircraft increasingly feature electronics that assist flight crews in performing their duties and reducing their fatigue. While these electronic devices improve aircraft performance, they also add greatly to the thermal load that must be managed within the aircraft. Cooling technologies currently used on aircraft are approaching their limits and other means are being considered, including vapor- compression refrigeration systems. However, unlike cooling systems used on Earth, systems employed on aircraft must meet rapidly changing conditions. For instance, as onboard electronic devices switch on and off, the energy they emit by heat transfer alters the thermal load; additionally, the temperature of the air outside the aircraft into which such waste heat is discarded changes with altitude and flight speed. Accordingly, for vapor-compression systems to be practical for aircraft use, engineers must determine if the systems can quickly adapt to rapidly changing thermal loads and temperatures. The object of this project is to develop the preliminary design of a bench-top laboratory set-up with which to evaluate the performance of a vapor-compression refrigeration system subject to broadly variable thermal inputs and changing ambient conditions. Document your design in a report having at least three references.