Moran M.J., Shapiro H.N. Fundamentals of Engineering Thermodynamics

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In obtaining these expressions, heat transfer with the surroundings and changes in

kinetic and potential energy have been ignored. The magnitude of the work devel-

oped by the turbine of a Brayton refrigeration cycle is typically significant relative to

the compressor work input.

Heat transfer from the cold region to the refrigerant gas circulating through the

low-pressure heat exchanger, the refrigeration effect, is

5 h

2 h

The coefficient of performance is the ratio of the refrigeration effect to the net

work input:

b 5

2 W

2 h

22 1h

2 h

(10.11)

In the next example, we illustrate the analysis of an ideal Brayton refrigeration

cycle.

Analyzing an Ideal Brayton Refrigeration Cycle

c c c c EXAMPLE 10.5 c

Air enters the compressor of an ideal Brayton refrigeration cycle at 1 atm, 480°R, with a volumetric flow rate

of 50 ft

/s. If the compressor pressure ratio is 3 and the turbine inlet temperature is 540°R, determine (a) the

net power input, in Btu/min, (b) the refrigeration capacity, in Btu/min, (c) the coefficient of performance.

SOLUTION

Known:

An ideal Brayton refrigeration cycle operates with air. Compressor inlet conditions, the turbine inlet

temperature, and the compressor pressure ratio are given.

Find: Determine the net power input, in Btu/min, the refrigeration capacity, in Btu/min, and the coefficient of

performance.

Schematic and Given Data:

Engineering Model:

Each component of the

cycle is analyzed as a con-

trol volume at steady state.

The control volumes are

indicated by dashed lines on

the accompanying sketch.

2. The turbine and compressor

processes are isentropic.

3. There are no pressure drops

through the heat exchangers.

4. Kinetic and potential energy

effects are negligible.

5. The working fluid is air

modeled as an ideal gas.

Fig. E10.5

540°R

480°R

p = 3 atm

p = 1 atm

4s 1

Heat exchanger

Turbine Compressor

out

cycle

540°R

(AV)

50 ft

480°R

1 atm

10.7 Gas Refrigeration Systems 613

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614 Chapter 10 Refrigeration and Heat Pump Systems

Analysis: The analysis begins by determining the specific enthalpy at each numbered state of the cycle. At state

1, the temperature is 4808R. From Table A-22E, h

5 114.69 Btu/lb, p

5 0.9182. Since the compressor process

is isentropic, h

can be determined by first evaluating p

at state 2s. That is

5 13210.918225 2.755

Then, interpolating in Table A-22E, we get h

5 157.1 Btu/lb.

The temperature at state 3 is given as T

5 5408R. From Table A-22E, h

5 129.06 Btu/lb, p

5 1.3860. The

specific enthalpy at state 4s is found by using the isentropic relation

5 p

5 11.3860211

325 0.462

Interpolating in Table A-22E, we obtain h

5 94.1 Btu/lb.

(a) The net power input is

cycle

5 m

31h

2 h

22 1h

2 h

This requires the mass flow rate m

, which can be determined from the volumetric flow rate and the specific

volume at the compressor inlet:

1AV2

Since y

5 1R

M2T

1AV2

M2T

150 ft

60 s

min

114.7 lbf

in.

144 in.

1545 ft ? lbf

28.97 lb ? 8R

b14808R2

5 248 lb

min

Finally

cycle

5 1248 lb

min231157.1 2 114.6922 1129.06 2 94.124 Btu

1848 Btu

min

(b) The refrigeration capacity is

5 m

2 h

5 1248 lb

min21114.69 2 94.12 Btu

5 5106 Btu

min

➊ b 5

cycle

5106

1848

5 2.76

➊ Irreversibilities within the compressor and turbine serve to decrease the

coefficient of performance significantly from that of the corresponding ideal

cycle because the compressor work requirement is increased and the turbine

work output is decreased. This is illustrated in Example 10.6.

Ability to…

❑

sketch the T–s diagram of the

ideal Brayton refrigeration

cycle.

❑

fix each of the principal states

and retrieve necessary

property data.

❑

calculate net power input,

refrigeration capacity, and

coefficient of performance.

✓

Skills Developed

Determine the refrigeration capacity in tons of refrigeration.

Ans. 25.53 ton.

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Example 10.6 illustrates the effects of irreversible compression and turbine expan-

sion Building on Example 10.5, on the performance of Brayton cycle refrigeration.

For this, we apply the isentropic compressor and turbine efficiencies introduced in

Sec. 6.12.

Evaluating Performance of a Brayton Refrigeration Cycle with Irreversibilities

Reconsider Example 10.5, but include in the analysis that the compressor and turbine each have an isentropic

efficiency of 80%. Determine for the modified cycle (a) the net power input, in Btu/min, (b) the refrigeration

capacity, in Btu/min, (c) the coefficient of performance, and discuss its value.

SOLUTION

Known:

A Brayton refrigeration cycle operates with air. Compressor inlet conditions, the turbine inlet tempera-

ture, and the compressor pressure ratio are given. The compressor and turbine each have an isentropic efficiency

of 80%.

Find: Determine the net power input and the refrigeration capacity, each in Btu/min. Also, determine the coef-

ficient of performance and discuss its value.

Schematic and Given Data:

Analysis:

(a) The power input to the compressor is evaluated using the isentropic compressor efficiency, h

. That is

The value of the work per unit mass for the isentropic compression, 1W

, is determined with data from

the solution in Example 10.5 as 42.41 Btu/lb. The actual power required is then

1248 lb

min2142.41 Btu

lb2

10.82

5 13,147 Btu

min

The turbine power output is determined using the turbine isentropic efficiency h

. Thus, W

5 h

Using data from the solution to Example 10.5 gives 1W

5 34.96 Btu

lb. The actual turbine work is then

5 m

5 1248 lb

min210.82134.96 Btu

lb2

6936

min

Engineering Model:

Each component of the cycle is analyzed as a control

volume at steady state.

2. The compressor and turbine are adiabatic.

3. There are no pressure drops through the heat exchangers.

4. Kinetic and potential energy effects are negligible.

5. The working fluid is air modeled as an ideal gas.

Fig. E10.6

= 480°R

= 540°R

p = 3 atm

p = 1 atm

c c c c EXAMPLE 10.6 c

10.7 Gas Refrigeration Systems 615

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616 Chapter 10 Refrigeration and Heat Pump Systems

The net power input to the cycle is

cycle

5 13,147 2 6936 5 6211 Btu

min

(b) The specific enthalpy at the turbine exit, h

, is required to evaluate the refrigeration capacity. This enthalpy

can be determined by solving W

5 m

2 h

2 to obtain h

5 h

2 W

. Inserting known values

5 129.06 2 a

6936

248

b5 101.1 Btu

The refrigeration capacity is then

5 m

2 h

25 124821114.69 2 101.125 3370 Btu

min

b 5

cycle

3370

6211

5 0.543

The value of the coefficient of performance in this case is less than unity. This

means that the refrigeration effect is smaller than the net work required to achieve

it. Additionally, note that irreversibilities in the compressor and turbine have a

significant effect on the performance of gas refrigeration systems. This is brought

out by comparing the results of the present example with those of Example 10.5.

Irreversibilities result in an increase in the work of compression and a reduction

in the work output of the turbine. The refrigeration capacity is also reduced. The

overall effect is that the coefficient of performance is decreased significantly.

Ability to…

❑

sketch the T–s diagram of

the Brayton refrigeration

cycle with irreversibilities in

the turbine and compressor.

❑

fix each of the principal

states and retrieve neces-

sary property data.

❑

calculate net power input,

refrigeration capacity, and

coefficient of performance.

✓

Skills Developed

Determine the coefficient of performance for a Carnot refrig-

eration cycle operating between reservoirs at 4808R and 5408R. Ans. 8.

10.7.2

Additional Gas Refrigeration Applications

To obtain even moderate refrigeration capacities with the Brayton refrigeration cycle,

equipment capable of achieving relatively high pressures and volumetric flow rates is

needed. For most applications involving air conditioning and for ordinary refrigeration

processes, vapor-compression systems can be built more cheaply and can operate with

higher coefficients of performance than gas refrigeration systems. With suitable mod-

ifications, however, gas refrigeration systems can be used to achieve temperatures of

about 21508C (22408F), which are well below the temperatures normally obtained

with vapor systems.

Figure 10.16 shows the schematic and T–s diagram of an ideal Brayton cycle modi-

fied by introduction of a heat exchanger. The heat exchanger allows the air exiting the

compressor at state 2 to cool below the warm region temperature T

, giving a low

turbine inlet temperature, T

. Without the heat exchanger, air could be cooled only

close to T

, as represented on the figure by state a. In the subsequent expansion through

the turbine, the air achieves a much lower temperature at state 4 than would have been

possible without the heat exchanger. Accordingly, the refrigeration effect, achieved from

state 4 to state b, occurs at a correspondingly lower average temperature.

An example of the application of gas refrigeration to cabin cooling in an aircraft

is illustrated in Fig. 10.17. As shown in the figure, a small amount of high-pressure air

is extracted from the main jet engine compressor and cooled by heat transfer to the

ambient. The high-pressure air is then expanded through an auxiliary turbine to the

pressure maintained in the cabin. The air temperature is reduced in the expansion

and thus is able to fulfill its cabin cooling function. As an additional benefit, the

turbine expansion can provide some of the auxiliary power needs of the aircraft.

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Size and weight are important considerations in the selection of equipment for use

in aircraft. Open-cycle systems, like the example given here, utilize compact high-

speed rotary turbines and compressors. Furthermore, since the air for cooling comes

directly from the surroundings, there are fewer heat exchangers than would be needed

if a separate refrigerant were circulated in a closed vapor-compression cycle.

10.7.3

Automotive Air Conditioning Using

Carbon Dioxide

Owing primarily to environmental concerns, automotive air-conditioning systems

using CO

are currently under active consideration. Carbon dioxide causes no harm

to the ozone layer, and its Global Warming Potential of 1 is small compared to that

of R-134a, commonly used in automotive air-conditioning systems. Carbon dioxide is

nontoxic and nonflammable. As it is abundant in the atmosphere and the exhaust gas

of coal-burning power and industrial plants, CO

is a relatively inexpensive choice as

a refrigerant. Still, automakers considering a shift to CO

away from R-134a must

Fig. 10.16 Brayton refrigeration cycle modified with a heat exchanger.

from refrigerated region

out

to warm region

out

cycle

Heat

exchanger

Turbine Compressor

Temperature of

warm region, T

Fig. 10.17 An application of gas

refrigeration to aircraft cabin cooling.

Auxiliary

power

Auxiliary

turbine

Air extracted for

cabin cooling

Heat transfer

to ambient

Main jet

engine

compressor

Ambient

air in

combustor

Cool air

to cabin

10.7 Gas Refrigeration Systems 617

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618 Chapter 10 Refrigeration and Heat Pump Systems

weigh system performance, equipment costs, and other key issues before embracing

such a change in longstanding practice.

Figure 10.18 shows the schematic of a CO

-charged automotive air-conditioning

system with an accompanying T–s diagram labeled with the critical temperature T

and critical pressure p

of CO

: 31°C (88°F) and 72.9 atm, respectively. The system

combines aspects of gas refrigeration with aspects of vapor-compression refrigeration.

Let us follow the CO

as it passes steadily through each of the components, beginning

with the inlet to the compressor.

Carbon dioxide enters the compressor as superheated vapor at state 1 and is com-

pressed to a much higher temperature and pressure at state 2. The CO

passes from

the compressor into the gas cooler, where it cools at constant pressure to state 3 as

a result of heat transfer to the ambient. The temperature at state 3 approaches that

of the ambient, denoted on the figure by T

. CO

is further cooled in the intercon-

necting heat exchanger at constant pressure to state 4, where the temperature is

below that of ambient. Cooling is provided by low-temperature CO

in the other

stream of the heat exchanger. During this portion of the refrigeration cycle, the pro-

cesses are like those seen in gas refrigeration.

This similarity ends abruptly as the CO

next expands through the valve to

state 5 in the liquid–vapor region and then enters the evaporator, where it is

vaporized to state 6 by heat transfer from the passenger cabin at temperature T

thereby cooling the passenger cabin. These processes are like those seen in vapor-

compression refrigeration systems. Finally, at state 6 the CO

enters the heat

exchanger, exiting at state 1. The heat exchanger increases the cycle’s perfor-

mance in two ways: by delivering lower-quality two-phase mixture at state 5,

increasing the refrigerating effect through the evaporator, and by producing

higher-temperature superheated vapor at state 1, reducing the compressor power

required.

Heat exchanger

Evaporator

Gas cooler

Expansion

valve

Compressor

out

(31°C, 88°F)

Ambient

temperature, T

Temperature of

passenger cabin, T

Fig. 10.18 Carbon dioxide automotive air-conditioning system.

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In this chapter we have considered refrigeration and heat pump

systems, including vapor systems where the refrigerant is alter-

nately vaporized and condensed, and gas systems where the

refrigerant remains a gas. The three principal types of systems

discussed are the vapor-compression, absorption, and reversed

Brayton cycles.

The performance of simple vapor refrigeration systems is

described in terms of the vapor-compression cycle. For this cycle,

we have evaluated the principal work and heat transfers along

with two important performance parameters: the coefficient of

performance and the refrigeration capacity. We have considered

the effect on performance of irreversibilities during the compres-

sion process and in the expansion across the valve, as well as

the effect of irreversible heat transfer between the refrigerant

and the warm and cold regions. Variations of the basic vapor-

compression refrigeration cycle also have been considered,

including cold storage, cascade cycles, and multistage compres-

sion with intercooling. A discussion of vapor-compression heat

pump systems is also provided.

Qualitative discussions are presented of refrigerant proper-

ties and of considerations in selecting refrigerants. Absorption

refrigeration and heat pump systems are also discussed quali-

tatively. The chapter concludes with a study of gas refrigeration

systems.

The following list provides a study guide for this chapter.

When your study of the text and end-of-chapter exercises has

been completed, you should be able to

write out the meanings of the terms listed in the margin

throughout the chapter and understand each of the related

concepts. The subset of key concepts listed below is particu-

larly important.

sketch the T–s diagrams of vapor-compression refrigeration

and heat pump cycles and of Brayton refrigeration cycles, cor-

rectly showing the relationship of the refrigerant temperature

to the temperatures of the warm and cold regions.

apply the first and second laws along with property data to

determine the performance of vapor-compression refrigera-

tion and heat pump cycles and of Brayton refrigeration cycles,

including evaluation of the power required, the coefficient of

performance, and the capacity.

sketch schematic diagrams of vapor-compression cycle modi-

fications, including cascade cycles and multistage compres-

sion with intercooling between the stages. In each case be

able to apply mass and energy balances, the second law, and

property data to determine performance.

explain the operation of absorption refrigeration systems.

c CHAPTER SUMMARY AND STUDY GUIDE

c KEY ENGINEERING CONCEPTS

vapor-compression refrigeration, p. 592

refrigeration capacity, p. 592

ton of refrigeration, p. 592

absorption refrigeration, p. 606

vapor-compression heat pump, p. 609

Brayton refrigeration cycle, p. 612

c KEY EQUATIONS

max

2 T

(10.1) p. 591 Coefficient of performance of the Carnot refrigera-

tion cycle (Fig. 10.1)

b 5

2 h

(10.7) p. 593 Coefficient of performance of the vapor-compression

refrigeration cycle (Fig. 10.3)

max

2 T

(10.9) p. 608 Coefficient of performance of the Carnot heat pump

cycle (Fig. 10.1)

g 5

out

2 h

(10.10) p. 609 Coefficient of performance of the vapor-compression

heat pump cycle (Fig. 10.13)

b 5

2 W

2 h

22 1h

2 h

(10.11) p. 613

Coefficient of performance of the Brayton refrigera-

tion cycle (Fig. 10.15)

Exercises: Things Engineers Think About 619

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620 Chapter 10

Refrigeration and Heat Pump Systems

c PROBLEMS: DEVELOPING ENGINEERING SKILLS

Vapor Refrigeration Systems

10.1 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°C and exits as saturated

liquid. The evaporator operates at 0°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.

evaporator.

10.2 Refrigerant 22 is the working fluid in a Carnot vapor

refrigeration cycle for which the evaporator temperature is

230°C. Saturated vapor enters the condenser at 36°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.

(d) the refrigeration capacity, in tons.

10.3 A Carnot vapor refrigeration cycle operates between

thermal reservoirs at 40°F and 90°F. For (a) Refrigerant 134a,

(b) propane, (c) water, (d) Refrigerant 22, and (e) ammonia

as the working fluid, determine the operating pressures in the

condenser and evaporator, in lbf/in.

, and the coefficient of

performance.

10.4 Consider a Carnot vapor refrigeration cycle with

Refrigerant 134a as the working fluid. The cycle maintains

a cold region at 40°F when the ambient temperature is

90°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 °R.

(b) compressor and turbine work, each in Btu per lb of

refrigerant flowing.

(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.

State p (lbf/in.

) h (Btu/lb) s (Btu/lb ? 8R)

1 40 104.12 0.2161

2 140 114.95 0.2161

3 140 44.43 0.0902

4 40 42.57 0.0902

10.5 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

5 90°F.

c EXERCISES: THINGS ENGINEERS THINK ABOUT

1. What are the temperatures inside the fresh food and

freezer compartments of your refrigerator? Do you know

what values are recommended for these temperatures?

2. You have a refrigerator located in your garage. Does

it perform differently in the summer than in the win-

ter? Explain.

3. Abbe installs a dehumidifier to dry the walls of a

small, closed basement room. When she enters the

room later, it feels warm. Why?

4. Why does the indoor unit of a central air conditioning

system have a drain hose?

5. Your air conditioner has a label that lists an EER of

10 Btu/h per watt. What does that mean?

6. Can the coefficient of performance of a heat pump

have a value less than one?

7. You see an advertisement for a natural gas–fired absorp-

tion refrigeration system. How can burning natural gas

play a role in achieving cooling?

8. What are n-type and p-type semiconductors?

9. What qualifies a refrigerator to be an Energy Star

appliance?

10. You see an advertisement claiming that heat pumps

are particularly effective in Atlanta, Georgia. Why might

that be true?

11. If your car’s air conditioner discharges only warm

air while operating, what might be wrong with it?

12. Large office buildings often use air conditioning to

cool interior areas even in winter in cold climates.

Why?

13. In what North American locations are heat pumps not

a good choice for heating dwellings? Explain.

14. If the heat exchanger is omitted from the system of

Fig. 10.16, what is the effect on the coefficient of per-

formance?

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10.6 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.

10.7 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.

10.8 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, 2128C, and

the condenser pressure is 9 bar. Liquid exits the condenser

at 328C. The mass flow rate of refrigerant is 7 kg/min.

Determine

(a) the compressor power, in kW.

(b) the refrigeration capacity, in tons.

10.9 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.

10.10 Refrigerant 22 enters the compressor of an ideal vapor-

compression refrigeration system as saturated vapor at

2408C with a volumetric flow rate of 15 m

/min. The

refrigerant leaves the condenser at 198C, 9 bar. Determine

(a) the compressor power, in kW.

(b) the refrigerating capacity, in tons.

10.11 An ideal vapor-compression refrigeration cycle, with

ammonia as the working fluid, has an evaporator temperature

of 2208C 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.

10.12 Refrigerant 134a enters the compressor of an ideal

vapor-compression refrigeration cycle as saturated vapor at

2108F. The condenser pressure is 160 lbf/in.

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 lbf/in.

to 908F.

10.13 To determine the effect of changing the evaporator

temperature 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 10.11 for saturated vapor entering the

compressor at temperatures ranging from 240 to 2108C. All

other conditions are the same as in Problem 10.11.

10.14 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

10.11 for condenser pressures ranging from 8 to 16 bar. All

other conditions are the same as in Problem 10.11.

10.15 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.

10.16 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 1008F. Determine, for the

modified cycle,

Condenser

Evaporator

Compressor

out

Hot region

Cold region

Expansion

valve

= 30.59

–––

min

State

---

Sat.

102.94

131.04

50.64

0.2391

0.1009

---

180

(lbf/in.

)

(Btu/lb)

(Btu/lb·°R)

T (°F)

Fig. P10.9

Problems: Developing Engineering Skills 621

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622 Chapter 10 Refrigeration and Heat Pump Systems

(a) the compressor power, in horsepower.

(b) the rate of heat transfer from the working fluid passing

through the condenser, in Btu/min.

(d) the rates of exergy destruction in the compressor and

expansion valve, each in Btu/min, for T

5 908F.

10.17 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.

(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.

Let T

5 21°C, p

5 1 bar.

State p (bar) T (°C) h (kJ/kg) s (kJ/kg ? K)

1 1.4 210 243.40 0.9606

2 7 58.5 295.13 1.0135

3 7 24 82.90 0.3113

4 1.4 218.8 82.90 0.33011

10.18 A vapor-compression refrigeration system, using

ammonia as the working fluid, has evaporator and condenser

pressures of 30 and 200 lbf/in.

, respectively. The refrigerant

passes through each heat exchanger with a negligible

pressure drop. At the inlet and exit of the compressor, the

temperatures are 108F and 3008F, respectively. The heat

transfer rate from the working fluid passing through the

condenser is 50,000 Btu/h, and liquid exits at 200 lbf/in.

908F. If the compressor operates adiabatically, determine

(a) the compressor power input, in hp.

(b) the coefficient of performance.

10.19 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 08C,

while discharging energy by heat transfer to the surrounding

air at 308C: Refrigerant 22, Refrigerant 134a, ammonia,

propane?

10.20 Consider the following vapor-compression refrigeration

cycle used to maintain a cold region at temperature T

when

the ambient temperature is 80°F: Saturated vapor enters the

compressor at 15°F below T

, and the compressor operates

adiabatically with an isentropic efficiency of 80%. Saturated

liquid exits the condenser at 958F. 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

ranging from 408F to 2258F if the

refrigerant is

(a) Refrigerant 134a.

(b) propane.

(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.

10.21 In a vapor-compression refrigeration cycle, ammonia

exits the evaporator as saturated vapor at 2228C. The

refrigerant enters the condenser at 16 bar and 1608C, 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 refrigerant, in kg/s.

(b) the power input to the compressor, in kW.

(d) the isentropic compressor efficiency.

10.22 A vapor-compression refrigeration system with a capacity

of 10 tons has superheated Refrigerant 134a vapor entering

the compressor at 158C, 4 bar, and exiting at 12 bar. The

compression process can be modeled by py

1.0 1

5 constant. At

the condenser exit, the pressure is 11.6 bar, and the temperature

is 448C. The condenser is water-cooled, with water entering at

208C and leaving at 308C with a negligible change in pressure.

Heat transfer from the outside of the condenser can be

neglected. Determine

(a) the mass flow rate of the refrigerant, in kg/s.

(b) the power input and the heat transfer rate for the

compressor, each in kW.

(d) the mass flow rate of the cooling water, in kg/s.

(e) the rates of exergy destruction in the condenser and

expansion valve, each expressed as a percentage of the

power input. Let T

5 208C.

10.23 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 658F and

leaving at 808F 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.

lb/min.

(d) the coefficient of performance.

State p (lbf/in.

) T (8F) h (Btu/lb)

1 38.4 0 193.2

2 180 120 229.8

3 180 85 74.41

4 38.4 0 74.41

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