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

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material structure, so electrons move freely and more rapidly through that material. When

power is provided by the power source, positively charged holes move in the direction of

current while negatively charged electrons move opposite to the current; each transfers

energy from the cold region to the warm region.

The process of Peltier refrigeration may be understood by following the journey of an

electron as it travels from the negative terminal of the power source to the positive terminal.

On flowing through the metallic interconnect and into the p-type material, the electron slows

and loses energy, causing the surrounding material to warm. At the other end of the p-type

material, the electron accelerates as it enters the metallic interconnect and then the n-type

material. The accelerating electron acquires energy from the surrounding material and

causes the end of the p-type leg to cool. While the electron traverses the p-type material

from the hot end to the cold end, holes are moving from the cold end to the hot end,

transferring energy away from the cold end. While traversing the n-type material from the cold

end to the hot end, the electron also transfers energy away from the cold end to the hot

end. When it reaches the warm end of the n-type leg, the electron flows through the metal-

lic interconnect and enters the next p-type material, where it slows and again loses energy.

This scenario repeats itself at each pair of p-type and n-type legs, resulting in more removal

of energy from the cold end and its deposit at the hot end. Thus, the overall effect of the

thermoelectric cooler is heat transfer from the cold region to the warm region.

These simple coolers have no moving parts at a macroscopic level and are compact.

They are reliable and quiet. They also use no refrigerants that harm the ozone layer or

contribute to global climate change. Despite such advantages, thermoelectric coolers

have found only specialized application because of low coefficients of performance com-

pared to vapor-compression systems. However new materials and production methods

may make this type of cooler more effective, material scientists report.

As shown in Fig. 10.7, at the core of a thermoelectric cooler are two dissimilar materials,

in this case n-type and p-type semiconductors. To be effective for thermoelectric cooling,

the materials must have low thermal conductivity and high electrical conductivity, a rare

combination in nature. However, new materials with novel microscopic structures at the

nanometer level may lead to improved cooler performance. With nanotechnology and other

advanced techniques, material scientists are striving to find materials with the favorable

characteristics needed to improve the performance of thermoelectric cooling devices.

10.4 Other Vapor-Compression Applications

The basic vapor-compression refrigeration cycle can be adapted for special applica-

tions. Three are presented in this section. The first is cold storage, which is a thermal

energy storage approach that involves chilling water or making ice. The second is a

combined-cycle arrangement where refrigeration at relatively low temperature is

achieved through a series of vapor-compression systems, with each normally employ-

ing a different refrigerant. In the third, compression work is reduced through multi-

stage compression with intercooling between stages. The second and third applications

considered are analogous to power cycle applications considered in Chaps. 8 and 9.

10.4.1

Cold Storage

Chilling water or making ice during off-peak periods, usually overnight or over week-

ends, and storing chilled water/ice in tanks until needed for cooling is known as cold

storage. Cold storage is an aspect of thermal energy storage considered in the box

on p. 111. Applications of cold storage include cooling of office and commercial buildings,

medical centers, college campus buildings, and shopping malls.

10.4 Other Vapor-Compression Applications 603

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604 Chapter 10

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Figure 10.8 illustrates a cold storage system intended for the comfort cooling of

an occupied space. It consists of a vapor-compression refrigeration unit, ice maker

and ice storage tank, and coolant loop. Running at night, when less power is required

for its operation due to cooler ambient temperatures and when electricity rates are

lowest, the refrigeration unit freezes water. The ice produced is stored in the accom-

panying tank. When cooling is required by building occupants during the day, the

temperature of circulating building air is reduced as it passes over coils carrying

chilled coolant flowing from the ice storage tank. Depending on local climate, some

moisture also may be removed or added (see Secs. 12.8.3 and 12.8.4). Cool storage

can provide all cooling required by the occupants or work in tandem with vapor-

compression or other comfort cooling systems to meet needs.

10.4.2

Cascade Cycles

Combined cycle arrangements for refrigeration are called cascade cycles. In Fig. 10.9 a

cascade cycle is shown in which two vapor-compression refrigeration cycles, labeled A and

B, are arranged in series with a counterflow heat exchanger linking them. In the interme-

diate heat exchanger, the energy rejected during condensation of the refrigerant in the

lower-temperature cycle A is used to evaporate the refrigerant in the higher-temperature

cycle B. The desired refrigeration effect occurs in the low-temperature evaporator, and heat

rejection from the overall cycle occurs in the high-temperature condenser. The coefficient

of performance is the ratio of the refrigeration effect to the total work input

b 5

1 W

Fig. 10.8 Cold storage applied to comfort cooling.

–

Return

refrigerant

Ice maker

Ice storage

Pump

Coolant loop

Condensate

Warm, humid air

from occupied spaces

Cool, less humid

air to occupied spaces

Chilled coolant

Cold

refrigerant

Refrigeration unit

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The mass flow rates in cycles A and B are normally different. However,

the mass flow rates are related by mass and energy rate balances on the

interconnecting counterflow heat exchanger serving as the condenser for

cycle A and the evaporator for cycle B. Although only two cycles are shown

in Fig. 10.9, cascade cycles may employ three or more individual cycles.

A significant feature of the cascade system illustrated in Fig. 10.9 is

that the refrigerants in the two or more stages can be selected to have

advantageous evaporator and condenser pressures in the two or more

temperature ranges. In a double cascade system, a refrigerant would be

selected for cycle A that has a saturation pressure–temperature relation-

ship that allows refrigeration at a relatively low temperature without

excessively low evaporator pressures. The refrigerant for cycle B would

have saturation characteristics that permit condensation at the required

temperature without excessively high condenser pressures.

10.4.3

Multistage Compression with Intercooling

The advantages of multistage compression with intercooling between

stages have been cited in Sec. 9.8, dealing with gas power systems. Inter-

cooling is achieved in gas power systems by heat transfer to the lower-

temperature surroundings. In refrigeration systems, the refrigerant tem-

perature is below that of the surroundings for much of the cycle, so

other means must be employed to accomplish intercooling and achieve

the attendant savings in the required compressor work input. An

arrangement for two-stage compression using the refrigerant itself for

intercooling is shown in Fig. 10.10. The principal states of the refrigerant

for an ideal cycle are shown on the accompanying T–s diagram.

Fig. 10.9 Example of a cascade vapor-

compression refrigeration cycle.

Low-temperature

evaporator

High-temperature

condenser

Intermediate

heat exchanger

Expansion

valve

Expansion

valve

Compressor

out

Cycle A

Cycle B

Fig. 10.10 Refrigeration cycle with two stages of compression and flash intercooling.

Compressor

out

Condenser

Evaporator

Direct contact

heat exchanger

Flash

chamber

Expansion

valve

Expansion

valve

(1)

(x)

(1)

(1 – x)

(1 – x

)

10.4 Other Vapor-Compression Applications 605

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606 Chapter 10

Refrigeration and Heat Pump Systems

Intercooling is accomplished in this cycle by means of a direct contact heat

exchanger. Relatively low-temperature saturated vapor enters the heat exchanger at

state 9, where it mixes with higher-temperature refrigerant leaving the first compres-

sion stage at state 2. A single mixed stream exits the heat exchanger at an intermedi-

ate temperature at state 3 and is compressed in the second compressor stage to the

condenser pressure at state 4. Less work is required per unit of mass flow for com-

pression from 1 to 2 followed by compression from 3 to 4 than for a single stage of

compression 1–2–a. Since the refrigerant temperature entering the condenser at state

4 is lower than for a single stage of compression in which the refrigerant would enter

the condenser at state a, the external irreversibility associated with heat transfer in

the condenser is also reduced.

A central role is played in the cycle of Fig. 10.10 by a liquid–vapor separator, called

a flash chamber. Refrigerant exiting the condenser at state 5 expands through a valve

and enters the flash chamber at state 6 as a two-phase liquid–vapor mixture with

quality x. In the flash chamber, the liquid and vapor components separate into two

streams. Saturated vapor exiting the flash chamber enters the heat exchanger at state

9, where intercooling is achieved as discussed above. Saturated liquid exiting the flash

chamber at state 7 expands through a second valve into the evaporator. On the basis

of a unit of mass flowing through the condenser, the fraction of the vapor formed in

the flash chamber equals the quality x of the refrigerant at state 6. The fraction of

the liquid formed is then (1 2 x). The fractions of the total flow at various locations

are shown in parentheses on Fig. 10.10.

flash chamber

10.5 Absorption Refrigeration

Absorption refrigeration cycles are the subject of this section. These cycles have some

features in common with the vapor-compression cycles considered previously but

differ in two important respects:

c One is the nature of the compression process. Instead of compressing a vapor

between the evaporator and the condenser, the refrigerant of an absorption system

is absorbed by a secondary substance, called an absorbent, to form a liquid solution.

The liquid solution is then pumped to the higher pressure. Because the average

specific volume of the liquid solution is much less than that of the refrigerant vapor,

significantly less work is required (see the discussion of Eq. 6.51b in Sec. 6.13.2).

Accordingly, absorption refrigeration systems have the advantage of relatively

small work input compared to vapor-compression systems.

c The other main difference between absorption and vapor-compression systems is

that some means must be introduced in absorption systems to retrieve the refriger-

ant vapor from the liquid solution before the refrigerant enters the condenser. This

involves heat transfer from a relatively high-temperature source. Steam or waste heat

that otherwise would be discharged to the surroundings without use is particularly

economical for this purpose. Natural gas or some other fuel can be burned to provide

the heat source, and there have been practical applications of absorption refrigera-

tion using alternative energy sources such as solar and geothermal energy.

The principal components of an absorption refrigeration system are shown sche-

matically in Fig. 10.11. In this case, ammonia is the refrigerant and water is the absor-

bent. Ammonia circulates through the condenser, expansion valve, and evaporator as

in a vapor-compression system. However, the compressor is replaced by the absorber,

pump, generator, and valve shown on the right side of the diagram.

c In the absorber, ammonia vapor coming from the evaporator at state 1 is absorbed

by liquid water. The formation of this liquid solution is exothermic. Since the amount

of ammonia that can be dissolved in water increases as the solution temperature

absorption refrigeration

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decreases, cooling water is circulated around the absorber to remove

the energy released as ammonia goes into solution and maintain the

temperature in the absorber as low as possible. The strong ammonia–

water solution leaves the absorber at point a and enters the pump,

where its pressure is increased to that of the generator.

c In the generator, heat transfer from a high-temperature source drives

ammonia vapor out of the solution (an endothermic process), leaving

a weak ammonia–water solution in the generator. The vapor liberated

passes to the condenser at state 2, and the remaining weak solution

at c flows back to the absorber through a valve. The only work input

is the power required to operate the pump, and this is small in com-

parison to the work that would be required to compress refrigerant

vapor between the same pressure levels. However, costs associated

with the heat source and extra equipment not required by vapor-com-

pressor systems can cancel the advantage of a smaller work input.

Ammonia–water systems normally employ several modifications of

the simple absorption cycle considered above. Two common modifica-

tions are illustrated in Fig. 10.12. In this cycle, a heat exchanger is included

between the generator and the absorber that allows the strong water–

ammonia solution entering the generator to be preheated by the weak

solution returning from the generator to the absorber, thereby reducing

the heat transfer to the generator, Q

. The other modification shown on

the figure is the rectifier placed between the generator and the condenser.

The function of the rectifier is to remove any traces of water from the

refrigerant before it enters the condenser. This eliminates the possibility

of ice formation in the expansion valve and the evaporator.

Another type of absorption system uses lithium bromide as the absor-

bent and water as the refrigerant. The basic principle of operation is the

same as for ammonia–water systems. To achieve refrigeration at lower

temperatures than are possible with water as the refrigerant, a lithium

bromide–water absorption system may be combined with another cycle

Fig. 10.11

Simple ammonia–water absorption refrigeration system.

Expansion

valve

Evaporator

Condenser

High-

temperature

source

Generator

Weak solution

Strong solution

Absorber

Valve

Pump

Refrigerated

region

Cooling

water

out

Fig. 10.12 Modified ammonia–water

absorption system.

Condenser

Expansion

valve

Evaporator Absorber

Valve

Pump

Heat

exchanger

Generator

Rectifier

out

10.5 Absorption Refrigeration 607

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608 Chapter 10

Refrigeration and Heat Pump Systems

using a refrigerant with good low-temperature characteristics, such as ammonia, to

form a cascade refrigeration system.

10.6 Heat Pump Systems

The objective of a heat pump is to maintain the temperature within a dwelling or

other building above the temperature of the surroundings or to provide a heat trans-

fer for certain industrial processes that occur at elevated temperatures. Heat pump

systems have many features in common with the refrigeration systems considered

thus far and may be of the vapor-compression or absorption type. Vapor-compression

heat pumps are well suited for space heating applications and are commonly used

for this purpose. Absorption heat pumps have been developed for industrial applica-

tions and are also increasingly being used for space heating. To introduce some aspects

of heat pump operation, let us begin by considering the Carnot heat pump cycle.

10.6.1

Carnot Heat Pump Cycle

By simply changing our viewpoint, we can regard the cycle shown in Fig. 10.1 as a

heat pump. The objective of the cycle now, however, is to deliver the heat transfer

out

to the warm region, which is the space to be heated. At steady state, the rate at

which energy is supplied to the warm region by heat transfer is the sum of the energy

supplied to the working fluid from the cold region,

, and the net rate of work input

to the cycle, W

. That is

out

1 W

(10.8)

The coefficient of performance of any heat pump cycle is defined as the ratio of

the heating effect to the net work required to achieve that effect. For the Carnot heat

pump cycle of Fig. 10.1

max

out

2 W

area 2

–a–b–3–2

area 1–2–3–4–1

which reduces to

max

2 s

2 T

2 s

2 T

(10.9)

This equation, which corresponds to Eq. 5.11, represents the maximum theoretical

coefficient of performance for any heat pump cycle operating between two regions

at temperatures T

and T

. Actual heat pump systems have coefficients of perfor-

mance that are lower than calculated from Eq. 10.9.

A study of Eq. 10.9 shows that as the temperature T

of the cold region decreases,

the coefficient of performance of the Carnot heat pump decreases. This trait is also

exhibited by actual heat pump systems and suggests why heat pumps in which the

role of the cold region is played by the local atmosphere (air-source heat pumps)

normally require backup systems to provide heating on days when the ambient tem-

perature becomes very low. If sources such as well water or the ground itself are used,

relatively high coefficients of performance can be achieved despite low ambient air

temperatures, and backup systems may not be required.

10.6.2

Vapor-Compression Heat Pumps

Actual heat pump systems depart significantly from the Carnot cycle model. Most

systems in common use today are of the vapor-compression type. The method of

analysis of vapor-compression heat pumps is the same as that of vapor-compression

Heat_Pump_Cycle

A.11 – All Tabs

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refrigeration cycles considered previously. Also, the previous discussions concerning

the departure of actual systems from ideality apply for vapor-compression heat pump

systems as for vapor-compression refrigeration cycles.

As illustrated by Fig. 10.13, a typical vapor-compression heat pump for space heating

has the same basic components as the vapor-compression refrigeration system: com-

pressor, condenser, expansion valve, and evaporator. The objective of the system is

different, however. In a heat pump system,

comes from the surroundings, and

out

is directed to the dwelling as the desired effect. A net work input is required to

accomplish this effect.

The coefficient of performance of a simple vapor-compression heat pump with

states as designated on Fig. 10.13 is

g 5

out

2 h

(10.10)

The value of g can never be less than unity.

Many possible sources are available for heat transfer to the refrigerant passing

through the evaporator, including outside air; the ground; and lake, river, or well

water. Liquid circulated through a solar collector and stored in an insulated tank also

can be used as a source for a heat pump. Industrial heat pumps employ waste heat

or warm liquid or gas streams as the low-temperature source and are capable of

achieving relatively high condenser temperatures.

In the most common type of vapor-compression heat pump for space heating, the

evaporator communicates thermally with the outside air. Such

air-source heat pumps

also can be used to provide cooling in the summer with the use of a reversing valve,

as illustrated in Fig. 10.14. The solid lines show the flow path of the refrigerant in the

heating mode, as described previously. To use the same components as an air condi-

tioner, the valve is actuated, and the refrigerant follows the path indicated by the

dashed line. In the cooling mode, the outside heat exchanger becomes the condenser,

and the inside heat exchanger becomes the evaporator. Although heat pumps can be

more costly to install and operate than other direct heating systems, they can be

competitive when the potential for dual use is considered.

Example 10.4 illustrates use of the first and second laws of thermodynamics

together with property data to analyze the performance of an actual heat pump cycle,

including cost of operation.

vapor-compression

heat pump

air-source heat pump

Fig. 10.13 Air-source vapor-compression heat pump system.

Inside

air

Outside

air

Condenser

Compressor

Evaporator

out

Expansion

valve

10.6 Heat Pump Systems 609

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610 Chapter 10 Refrigeration and Heat Pump Systems

Fig. 10.14 Example of an air-to-air reversing

heat pump.

Expansion

valve

Outside

heat exchanger

Inside

heat exchanger

Reversing

valve

Compressor

Heating mode

Cooling mode

Analyzing an Actual Vapor-Compression Heat Pump Cycle

c c c c EXAMPLE 10.4 c

Refrigerant 134a is the working fluid in an electric-powered, air-source heat pump that maintains the inside tempera-

ture of a building at 228C for a week when the average outside temperature is 58C. Saturated vapor enters the com-

pressor at 288C and exits at 508C, 10 bar. Saturated liquid exits the condenser at 10 bar. The refrigerant mass flow

rate is 0.2 kg/s for steady-state operation. Determine (a) the compressor power, in kW, (b) the isentropic compressor

efficiency, (c) the heat transfer rate provided to the building, in kW, (d) the coefficient of performance, and (e) the

total cost of electricity, in $, for 80 hours of operation during that week, evaluating electricity at 15 cents per kW

SOLUTION

Known:

A heat pump cycle operates with Refrigerant 134a. The states of the refrigerant entering and exiting the

compressor and leaving the condenser are specified. The refrigerant mass flow rate and interior and exterior

temperatures are given.

Find: Determine the compressor power, the isentropic compressor efficiency, the heat transfer rate to the build-

ing, the coefficient of performance, and the cost to operate the electric heat pump for 80 hours of operation.

Schematic and Given Data:

Fig. E10.4

Condenser

Evaporator

Compressor

out

Building inside T

inside

= 22°C

outside

= 5°C

outside

= 5°C

inside

= 22°C

= 10 bar

Outside

Expansion

valve

50°C

–

8°C

4 1

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Engineering Model:

Each component of the cycle is analyzed as a control volume at steady state.

2. There are no pressure drops through the evaporator and condenser.

3. The compressor operates adiabatically. The expansion through the valve is a throttling process.

4. Kinetic and potential energy effects are negligible.

5. Saturated vapor enters the compressor and saturated liquid exits the condenser.

6. For costing purposes, conditions provided are representative of the entire week of operation and the

value of electricity is 15 cents per kW

Analysis: Let us begin by fixing the principal states located on the accompanying schematic and T–s diagram.

State 1 is saturated vapor at 288C; thus h

and s

are obtained directly from Table A-10. State 2 is superheated

vapor; knowing T

and p

, h

is obtained from Table A-12. State 3 is saturated liquid at 10 bar and h

is obtained

from Table A-11. Finally, expansion through the valve is a throttling process; therefore, h

5 h

. A summary of

property values at these states is provided in the following table:

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

1 28 2.1704 242.54 0.9239

2 50 10 280.19 —

3 — 10 105.29 —

4 — 2.1704 105.29 —

(a) The compressor power is

5 m

2 h

25 0.2

1280.19 2 242.542

1 kW

1 kJ

`5 7.53 kW

(b) The isentropic compressor efficiency is

2 h

where h

is the specific entropy at state 2s, as indicated on the accompanying

T–s diagram. State 2s is fixed using p

and s

5 s

. Interpolating in Table A-12,

5 274.18 kJ/kg. Solving for compressor efficiency

2 h

274.18 2 242.54

280.19 2 242.54

5 0.84 184%2

out

5 m

2 h

25 a0.2

b1280.19 2 105.292

1 kW

1 kJ

`5 34.98 kW

(d) The heat pump coefficient of performance is

g 5

out

34.98 kW

7.53 kW

5 4.65

(e) Using the result from part (a) together with the given cost and use data

3electricity cost for 80 hours of operation45 17.53 kW2180 h2

0.15

kW ? h

5 $90.36

Ability to…

❑

sketch the T–s diagram of

the vapor-compression heat

pump cycle with irreversibili-

ties in the compressor.

❑

fix each of the principal

states and retrieve

necessary property data.

❑

calculate the compressor

power, heat transfer rate

delivered, and coefficient

of performance.

❑

calculate isentropic

compressor efficiency.

❑

conduct an elementary

economic evaluation.

✓

Skills Developed

If the cost of electricity is 10 cents per kW

h, which is the

U. S. average for the period under consideration, evaluate the cost to operate

the heat pump, in $, keeping all other data the same. Ans. $60.24.

10.6 Heat Pump Systems 611

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612 Chapter 10 Refrigeration and Heat Pump Systems

10.7 Gas Refrigeration Systems

All refrigeration systems considered thus far involve changes in phase. Let us now

turn to

gas refrigeration systems in which the working fluid remains a gas throughout.

Gas refrigeration systems have a number of important applications. They are used to

achieve very low temperatures for the liquefaction of air and other gases and for

other specialized applications such as aircraft cabin cooling. The Brayton refrigeration

cycle illustrates an important type of gas refrigeration system.

10.7.1

Brayton Refrigeration Cycle

The Brayton refrigeration cycle is the reverse of the closed Brayton power cycle intro-

duced in Sec. 9.6. A schematic of the reversed Brayton cycle is provided in Fig. 10.15a.

The refrigerant gas, which may be air, enters the compressor at state 1, where the

temperature is somewhat below the temperature of the cold region, T

, and is com-

pressed to state 2. The gas is then cooled to state 3, where the gas temperature

approaches the temperature of the warm region, T

. Next, the gas is expanded to state

4, where the temperature, T

, is well below that of the cold region. Refrigeration is

achieved through heat transfer from the cold region to the gas as it passes from state

4 to state 1, completing the cycle. The T–s diagram in Fig. 10.15b shows an ideal Brayton

refrigeration cycle, denoted by 1–2s–3–4s–1, in which all processes are assumed to be

internally reversible and the processes in the turbine and compressor are adiabatic.

Also shown is the cycle 1–2–3–4–1, which suggests the effects of irreversibilities during

adiabatic compression and expansion. Frictional pressure drops have been ignored.

CYCLE ANALYSIS. The method of analysis of the Brayton refrigeration cycle is

similar to that of the Brayton power cycle. Thus, at steady state the work of the

compressor and the turbine per unit of mass flow are, respectively

5 h

2 h



and





5 h

2 h

gas refrigeration systems

Brayton refrigeration cycle

Fig. 10.15 Brayton refrigeration cycle.

Heat exchanger

Turbine Compressor

out

cycle

– W

··

Warm region

at T

Cold region

at T

(a)

Constant pressure

(b)

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