HEAT ENGINES AND REFRIGERATORS

THERMODYNAMICS

Department of Physics, Faculty of Science

Jazan University, KSA

Part-6

222 PHYS

Heat engine: Is a device that transforms heat partly

into work (mechanical energy) by a working

substance undergoing a cyclic process.

Several hundreds atmospheres and

water vaporizes at about 500 ªC

Schematic drawing of a steam engine.

Various statements of the second law

So far we have presented three statements of the second law of thermodynamics.

1. The entropy of the system never decreases,

2. You can not change heat energy into work with

100% efficiency. That is, there are no perfect engines.

3. You can not transfer heat energy from a low- temperature reservoir to a higher temperature reservoir without doing work. That is, there are no

perfect refrigerators.

0S

---Kelvin version

---Clausius version

We assume that all thermodynamic processes are reversible.

Carnot engine

CARNOT CYCLE

- Heat engine with the maximum possible efficiency

consistent with 2nd law.

- All thermal processes in the cycle must be reversible

- All heat transfer must occur (isothermally) because

conversion of work into heat is irreversible.

- When the temperature of the working substances

changes, there must be zero heat exchange

(adiabatic process).

- Carnot cycle – consists of two reversible isotherms

and two reversible adiabats

Qh = heat taken from heat

source

Qc = heat removed to heat sink

W = Work done

Th = temperature of heat source

TC = temperature of heat sink

Sadi Carnot (1824) Frenchman

Tc

Th

V

P Isothermal Expansion

Adiabatic Expansion

Isothermal

Compression

Adiabatic Compression

The Carnot Cycle

The purpose of an engine is to transform as much of the extracted heat

into work as possible.

We define “thermal efficiency as

h cW Q Q

HQ

. .

. . . h

Wenergy you get

energy you pay for Q

1 1c c

h h h

Q TW

Q Q T

Efficiency of a Carnot engine

In practice, the Carnot cycle cannot be used for a heat engine because the

slopes of the adiabatic and isothermal lines are very similar and the net work

output (area enclosed by PV diagram) is too small to overcome friction & other

losses in a real engine.

Efficiency of Carnot engine - max possible efficiency

for a heat engine operating between Tc and Th

The Carnot Cycle: Derivation of Maximum efficiency for a heat engine.

Carnot cycle is a reversible cycle between two heat reservoirs

1

2ln2

1 V

VTRndVPWQ h

V

Vgasbyh

4

3ln4

3 V

VTRndVPWQ c

V

Vgasonc

Isothermal processes

Adiabatic processes

1

4

1

1

1

3

1

2

VTVT

VTVT

ch

ch

4

3

1

2

1

4

1

3

1

1

1

2

V

V

V

V

V

V

V

V

2

1

2

1

ln

ln

c

c c

h hh

VT

Q TV

VQ TT

V

1 1h c c c

h h h h

Q Q Q TW

Q Q Q T

V

p

21

34

1 and 2: “cold”

3 and 4: “hot”

hh

h

QS

T

C

CC

T

QS

hQ

CQ

W

en

tro

py

heat

work

heat

hot reservoir, Th

cold reservoir, TC

Perfect Engines (no extra S generated)

The condition of continuous operation:

c chh c c h

h c h

Q TQS S Q Q

T T T

The work generated during one cycle of a

reversible process:

h ch c h

h

T TW Q Q Q

T

Carnot efficiency

the highest possible value of the energy conversion

efficiencymax 1 1c

h h

TW

Q T

This is the absolute max efficiency of a heat engine

Carnot Engine

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Temperature TH (oC)

eff

icie

nc

y

Per

pet

ual

mo

tion m

achin

e

Real Engines

Real heat engines have lower efficiencies because the processes within the

devices are not perfectly reversible

The entropy will be generated by irreversible processes:

max1 c

h h

TW

Q T

η = ηmax only in the limit of reversible operation.

Refrigerators, Air conditioners and Heat Pumps

Refrigerators or air conditioners

Coefficient of

Performance

W

QCOP c

Second Law of Thermodynamics. Refrigerators. Heat PumpsSchematic representation of a

refrigerator.

Entropy and the performance of refrigerators

The Carnot refrigerator

Adjacent fig., shows the basic elements of a

refrigerator. We call it a Carnot refrigerator. W

hT

cT

cQ

hQ

AB

CD

0 AVBV CVDV

AP

BP

CPDP

hT

cT

cQ

hQch

h c

QQ

T T

are satisfied.

h cW Q Q

Let’s define the “Coefficient of Performance”

cQwhat you wantCOP

what you pay for W

h cW Q Q Q

c

h c

QCOP

Q Q

ch

h c

QQ

T TQ

c

h c

TCOP

T T

for Carnot refrigerator

HW

Example-1

A “perfect” heat engine with η = 0.4 is used as a refrigerator

(the heat reservoirs remain the same). How much heat QC can

be transferred in one cycle from the cold reservoir to the hot

one if the supplied work in one cycle is W =10 kJ?

H C

H H

Q QW

Q Q

H

C

H

C

CH

cc

Q

Q

Q

Q

QQ

Q

W

QCOP

1

1C

H

Q

Q 1 1 0.6

1.51 1 0.4

COP

kJ 15cycle) one(in COPWQC

Example-2 A household refrigerator, COP =4.5, extracts heat from the

food chamber at the rate of .

(a) how much work per cycle is required to operate the refrigerator?

(b) how much heat per cycle is discharged to the room?

cycleJ /250

Solution:

(a)

(b)

4.5cQ

COPW

cycleJcycleJ

W /535.4

)/250(

303 /h cQ Q W J cycle

ch QQW

Work done by engine each cycle

h

W

Q

J 470J 890W J 420

The efficiency of the engine

J 908

J 420 % 2.47 472.0

Th= 550 K

Tc

Engine

Qh

Qc

W

= 470 J

= 890 J

For the engine shown in the figureExample-3a:

Example-3b: The engine ejects heat at 10 oC . Find the temperature of the hot

reservoir?

h

c

h

c

T

T

Q

Q

c

hch

Q

QTT

J 550

J 900K 283

hT K 463 C 190

o

Tc

Engine

Qh

Qc

W

= 550J

= 900 J

For the engine shown in the figure

Example-4: A Carnot engine operates

between a hot reservoir at 650 K and a cold

reservoir at 300 K. If it absorbs 400 J of heat

at the hot reservoir, how much work does it

deliver?

Th= 650 K

Tc= 300 K

Engine

Qh

Qc

W = ?

= 400 J

h

W

Q

h

ch

T

TT

h

chh

T

TTQW

K 650

K 300K 650J 400W J 215

Example-5: If the theoretical efficiency of a Carnot engine is to be 100%, the heat

sink must be

(A) at absolute zero.

(B) at 0°C.

(C) at 100°C.

(D) infinitely hot.

Example-6: A Carnot cycle consists of :

(A) two adiabats and two isobars.

(B) two isobars and two isotherms.

(C) two isotherms and two isomets.

(D) two adiabats and two isotherms.

Example-7: The temperature inside the engine of a helicopter is 20000C, the

temperature of the exhaust gases is 9000C. The mass of the helicopter is M =

2×103 kg, the heat of combustion of gasoline is qcomb = 47×103 kJ/kg, and the

density of gasoline is = 0.8 g/cm3. What is the maximum height that the

helicopter can reach by burning V = 1 liter of gasoline?

The work done on lifting the helicopter: MgHW

1 C

H H

TW

Q T For the ideal Carnot cycle (the maximum efficiency):

VqQ combH The heat released in the gasoline combustion:

mK

K

m/skg

literkg/liter0.8kJ/kg2

9282273

11731

8.92000

110471

1

3

H

Ccomb

comb

H

C

T

T

Mg

VqH

VqT

TMgH

Thus, H

H

C QT

TW

1