Heat engine-introduction

1. HE2 Thermal Physics

2. HE2 Thermal Physics
Heat Engine
• A heat engine is a device that absorbs heat (Q) and uses it
to do useful work (W) on the surroundings when operating
in a cycle.
• Sources of heat include the combustion of coal,
petroleum or carbohydrates and nuclear reactions.
• Working substance: the matter inside the heat engine
that undergoes addition or rejection of heat and that does
work on the surroundings. Examples include air and water
vapour (steam).
• In a cycle, the working substance is in the same
thermodynamic state at the end as at the start.

3. HE2 Thermal Physics
Heat Engine
E
Hot Body
(source of heat)
Q1
Cold Body
(absorbs heat)
Q2
W

4. HE2 Thermal Physics
Open system
Example of a Heat Engine

5. HE2 Thermal Physics
a
d
Internal Combustion Engine

6. HE2 Thermal Physics
Comparison of Otto and Diesel Cycles
combustion
Q=0
Q=0
Work per cycle
= Area inside

7. HE2 Thermal Physics
Nuclear Power Plant: A Very Large Heat Engine

8. HE2 Thermal Physics
Heat Engine
E
Hot Body
(source of heat)
Q1
Cold Body
(absorbs heat)
Q2
W

9. HE2 Thermal Physics
Efficiency of a Heat Engine
Efficiency, η = Work out/Heat in:
Apply First Law to the working substance:
∆U = Q1 – Q2 – W
But in a cycle, ∆U = 0
Thus, W = Q1 – Q2.
1
2
1
21
1
1
Q
Q
Q
QQ
Q
W
−=
−
==ηSubstituting:
1Q
W
=η
Lesson: η is maximum when Q2 is minimum.

10. HE2 Thermal Physics
The Stirling Engine
•Closed system
•Operates between two bodies with (small) different temperatures.
• Can use “stray” heat
See: http://www.animatedengines.com/ltdstirling.shtml

11. HE2 Thermal Physics
isothermal
isothermal
= air temp
=hot water
Heat in
Heat out
TH >TC
The Stirling Cycle
(TH - TC ) is proportional
to the amount of work
that is done in a cycle.
2

12. HE2 Thermal Physics

13. HE2 Thermal Physics
Carnot Cycle
Hot Reservoir
T1
Cold Reservoir
T2
C
Q1
Q2
W

14. HE2 Thermal Physics
Volume
Pressure
•
•
a
b
•
d
T1
Q1
Carnot Cycle
Q2
V
nRT
P 1
=
γ
V
const
P
.
=
T2
•c
Q=0
Q=0
V
nRT
P 2
=

15. HE2 Thermal Physics
Volume
Pressure
•
•
a
b
•
d
T1
Q1
Q2
V
nRT
P 1
=
γ
V
const
P
.
=
T2
•c
Q=0
Q=0
V
nRT
P 2
=
W
Carnot Cycle

16. HE2 Thermal Physics
From a to b: isothermal, so that ∆U = 0 and Q = - W
Thus, Q1 = +nRT1ln(Vb/Va) (+ve quantity)
Carnot Cycle
Similarly, from c to d: isothermal, so that ∆U = 0 and Q = - W
Thus, Q2 = +nRT2ln(Vd/Vc) = -nRT2ln(Vc/Vd) (-ve)
From b to c: adiabatic, Q = 0, so that TVγ-1
is constant.
Thus, T1Vb
γ-1
= T2Vc
γ-1
or 1
2
1
−






=
γ
b
c
V
V
T
T
Similarly, d to a: adiabatic, Q = 0, so that TVγ-1
is constant.
Thus, T2Vd
γ-1
= T1Va
γ-1
or 1
2
1
−






=
γ
a
d
V
V
T
T

17. HE2 Thermal Physics
Carnot Cycle
We see that:
11
2
1
−−






=





=
γγ
a
d
b
c
V
V
V
V
T
T
)/ln(
)/ln(
)/ln(
)/ln(
2
1
2
1
2
1
dc
ab
dc
ab
VVT
VVT
VVnRT
VVnRT
Q
Q
==
a
b
d
c
V
V
V
V
=
Which means that
Now also:
This is an important result. Temperature can be defined (on the
absolute (Kelvin) scale) in terms of the heat flows in a Carnot
Cycle.
But as the volume
ratios are equal: 2
1
2
1
T
T
Q
Q
=

18. HE2 Thermal Physics
What’s Special about a Carnot Cycle?
(1) Heat is transferred to/from only two reservoirs at fixed
temperatures, T1 and T2 - not at a variety of temperatures.
(2) Heat transfer is the most efficient possible because the
temperature of the working substance equals the temperature
of the reservoirs. No heat is wasted in flowing from hot to cold.
(3) The cycle uses an adiabatic process to raise and lower the
temperature of the working substance. No heat is wasted in
heating up the working substance.
(4) Carnot cycles are reversible. Not all cycles are!

19. HE2 Thermal Physics
What’s Special about a Carnot Cycle?
(5) The Carnot theorem states that the Carnot cycle (or any
reversible cycle) is the most efficient cycle possible. The Carnot
cycle defines an upper limit to the efficiency of a cycle.
• Where T1 and T2 are the temperatures of the hot and cold
reservoirs, respectively, in degrees Kelvin.
⇒ As T2 > 0, ηc is always <1.
• Recall that for any cycle, the efficiency of a heat engine is
given as:
1
2
1
1==
Q
Q
Q
W
Eη
• For an engine using a Carnot cycle, the efficiency is also
equal to:
1
2
1=
T
T
Cη

20. HE2 Thermal Physics
Efficiency of a Stirling Engine
Question: What is the maximum possible efficiency of a
Stirling engine operating between room temperature (25 °C)
and boiling water (100 °C)?
Question: What is the maximum possible efficiency of a
Stirling engine operating between room temperature (25 °C)
and ice (0 °C)?
Maximum efficiency would be achieved by a Carnot cycle
operating between reservoirs at T1 = 373 K and T2 = 298 K.
1
=20.0=
373
298
1=
Q
W
cη
1
=08.0=
298
273
1=
Q
W
cη

21. HE2 Thermal Physics
Kelvin-Planck Statement of the Second Law of
Thermodynamics
“It is impossible to construct a device that - operating in a
cycle - will produce no other effect than the extraction of
heat from a single body and the performance of an
equivalent amount of work”
Or…A cyclical engine cannot convert heat from a single
body completely into work. Some heat must be rejected
at a lower temperature. Thus, efficiency, η < 1!

22. HE2 Thermal Physics
Heat Engine
E
Hot Body
(source of heat)
Q1
Cold Body
(absorbs heat)
Q2 = 0
W= -Q1

23. HE2 Thermal Physics
Heat Engine
E
Hot Body
(source of heat)
Q1= 0
Cold Body
(absorbs heat)
Q2 = W
WPOSSIBLE!
Examples: friction
creating heat;
isothermal
compression of ideal
gas

24. HE2 Thermal Physics
Refrigerator: A heat engine operating in reverse
E
Hot Body
Q1
Cold Body
Q2
W
W
Q
work
heat
in
out
R
2
==η
Refrigerator Efficiency:

25. HE2 Thermal Physics
Refrigerator Efficiency
W
Q
work
heat
in
out
R
2
==η
21
2
QQ
Q
R
−
=η
21
2
TT
Tc
R
−
=η
First Law tells us that Q2 + W -Q1 = 0.
Thus, W = Q1 – Q2
2
21
2
1
2
1
2
21
11
1
T
TT
T
T
Q
Q
Q
QQ
c
R
−
=−=−=
−
=
η
For a Carnot refrigerator, the efficiency is:
Efficiency is usually >1!
The smaller the T difference, the more efficient is the
refrigerator.

26. HE2 Thermal Physics
Clausius Statement of the Second Law of
Thermodynamics
(applies to refrigerators)
“It is impossible to construct a device that - operating in a
cycle - will produce no other effect than heat transfer from
a colder body to hotter body.”
“Or…Heat cannot flow from a cold body to a hotter body
by itself. Work has to be done in the process.”

27. HE2 Thermal Physics

28. HE2 Thermal Physics
Efficiency of a Heat Pump
The purpose of a heat pump is to extract heat from a cold body (such
as the River Thames) and “pump” it to a hot body (such as an office
building).
The First Law tells us that W = Q1-Q2 So, substituting, we find:
1221
1
21
1
/1
1
TTTT
T
QQ
QC
hp
−
=
−
=
−
=η
ηhp is always > 1! For maximum η, T2 should be ≅ T1 (just slightly less).
W
QC
hp
1
=η
The efficiency is defined as the amount of heat pumped in to the hot
body per the amount of work done: