Heat Engine Introduction
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Transcript of Heat Engine Introduction
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HE2 Thermal Physics
Heat Engine
E
Hot ody(source of heat)
*+
,old ody(absorbs heat)
Q2
$
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HE2 Thermal Physics
Open system
Example of a Heat Engine
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HE2 Thermal Physics
a
d
Internal CombustionEngine
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HE2 Thermal Physics
Comparison of Otto and Diesel Cycles
combustion
Q=0
Q=0
Work per cycle
= Area inside
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HE2 Thermal Physics
Nuclear Power Plant: A ery !arge HeatEngine
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HE2 Thermal Physics
Heat Engine
E
Hot ody(source of heat)
Q+
,old ody(absorbs heat)
Q2
W
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HE2 Thermal Physics
E"ciency of a HeatEngine
E-ciency# η = $ork out.Heat in%
Aly /irst 0aw to the workingsubstance%
∆U 1 Q+ Q2 W ut in a cycle# ∆U 1 3
Thus# $ 1 *+ *2!
1
2
1
21
1
1
Q
Q
Q
QQ
Q
W −=
−
==η "ubstituting%
1Q
W =
η
0esson% η is ma'imum when Q2 is minimum!
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HE2 Thermal Physics
#$e %tirlingEngine
•,losed system
•4erates between two bodies with (small) di5erent
temeratures!
"ee%htt%..www!animatedengines!com.ltdstirling!shtml
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HE2 Thermal Physics
isothermal
isothermal
1 air tem
1hotwater
Heatin
Heatout
T H8T
,
#$e %tirling Cycle
(T H 9 T , ) is
roortional to theamount of work
that is done in acycle!
2
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HE2 Thermal Physics
Carnot Cycle
Hot :eservoirT +
,old :eservoirT 2
,
Q+
Q2
W
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HE2 Thermal Physics;olume
Pressure
•
•
a
b
•d
T 1
Q1
Carnot Cycle
Q2
V
nRT P
1=
γ V
const P
.=
T 2•c
Q=0Q=0
V
nRT P
2=
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HE2 Thermal Physics;olume
Pressure
•
•
a
b
•d
T 1
Q1
Q2
V
nRT P
1=
γ V
const P
.=
T 2•c
Q=0Q=0
V
nRT P
2=
W
Carnot Cycle
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HE2 Thermal Physics
Carnot Cycle
$e see that%
11
2
1
−−
=
=
γ γ
a
d
b
c
V V
V V
T T
a
b
d
c
V
V
V
V =
$hich means that
>ow also%)/ln(
)/ln(
)/ln(
)/ln(
2
1
2
1
2
1
d c
ab
d c
ab
V V T
V V T
V V nRT
V V nRT
Q
Q==
This is an imortant result! Temerature can bede?ned (on the absolute (@elvin) scale) in terms of
the heat ows in a ,arnot ,ycle!
ut as thevolume ratiosare e=ual%
2
1
2
1
T T
QQ =
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HE2 Thermal Physics
($at)s %pecial about aCarnot Cycle*
+,- Heat is transferred to.from only two reservoirsat fxed temeratures# T + and T 2 9 not at a variety of
temeratures!
+.- Heat transfer is the most e-cient ossiblebecause the temerature of the working substancee=uals the temerature of the reservoirs! >o heatis wasted in owing from hot to cold!
+/- The cycle uses an adiabatic rocess to raiseand lower the temerature of the workingsubstance! >o heat is wasted in heating u theworking substance!
+0- ,arnot cycles are reversible! >ot all cycles areB
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HE2 Thermal Physics
E"ciency of a %tirling Engine
1uestion: $hat is the ma'imum ossible
e-ciency of a "tirling engine oerating betweenroom temerature (2C ,) and boiling water (+33,)F
1uestion: $hat is the ma'imum ossible
e-ciency of a "tirling engine oerating betweenroom temerature (2C ,) and ice (3 ,)F
Ga'imum e-ciency would be achieved by a Carnotcycle oerating between reservoirs at T+ 1 I @
and T2 1 2JK @!
1
=20.0=373
2981=
Q
W cη
1
=08.0=298
2731=
Q
W cη
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HE2 Thermal Physics
2el3in4Planc5 %tatement of t$e%econd !aw of #$ermodynamics
6t is imossible to construct a device that 9oerating in a cycle 9 will roduce no other
e5ect than the e'traction of heat from a singlebody and the erformance of an e=uivalentamount of work7
Or LA cyclical engine cannot convert heat
from a single body comletely into work!"ome heat must be re&ected at a lowertemerature! Thus# e-ciency# η D +B
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HE2 Thermal Physics
6efrigerator: A $eat engine operating inre3erse
E
Hot ody
Q+
,old ody
Q2
W
W
Q
work
heat
in
out
R
2==η
Refrigerator Efficiency:
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HE2 Thermal Physics
6efrigerator E"ciency
W
Q
work
heat
in
out
R
2==η
21
2
QQQ R−
=η
/irst 0aw tells us that Q2 < W 9Q+ 1 3!
Thus# W 1 Q+ Q2
2
21
2
1
2
1
2
21
11
1
T
T T
T
T
Q
Q
Q
QQ
c R
−
=−=−=
−
=η
/or a ,arnot refrigerator# the e-ciency is%
21
2
T T
T c R −
=η E-ciency is usually 8+B
The smaller the T di5erence# the more
e-cient is the refrigerator!
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HE2 Thermal Physics
Clausius %tatement of t$e %econd!aw of #$ermodynamics
(alies to refrigerators)
6t is imossible to construct a device that 9
oerating in a cycle 9 will roduce no othere5ect than heat transfer from a colder body tohotter body!7
64rLHeat cannot ow from a cold body to ahotter body by itself! $ork has to be done inthe rocess!7
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E"ciency of a Heat Pump
The urose of a heat um is to e'tract heat from acold body (such as the :iver Thames) and 6um7 it toa hot body (such as an o-ce building)!
The /irst 0aw tells us that W 1 Q+9Q
2"o#
substituting# we ?nd%
1221
1
21
1
/1
1
T T T T
T
QQ
QC hp −
=−
=−
=η
η hp is always 8 +B /or ma'imum η , T 2 should be ≅ T + (&ustslightly less)
W
QC hp
1=η
The e-ciency is de?ned as the amount of heat umedin to the hot body er the amount of work done%
