Heat engines, Heat pumbs, Refrigerators
Trang 1LECTURE 9 HEAT ENGINES,
HEAT PUMPS, REFRIGERATORS
Lecturer: Tran Thi Ngoc Dung
Trang 2heat engine
• A heat engine is a device that takes
in energy by heat and, operating in a cyclic process, expels a fraction of that energy by means of work
• A heat engine carries some working substance through a cyclic process during which
• (1) the working substance absorbs
energy by heat from a high-temperature energy reservoir,
• (2) work is done by the engine,
• (3) energy is expelled by heat to a
lower-temperature reservoir
Trang 3The Efficiency of a Heat Engine
h
Q
' W reservoir
_ hot _ from _
received _
Heat
engine _
the _ by _ done _
Work
The Efficiency of an Engine
Engine operates in a cycle process, the change in internal energy is 0:
' c h
c
h Q Q Q Q
W '
Work done by the
engine:
0 W
Q Q
h
' c h
' c h
Q 1
Q
Q
Q Q
' W
Trang 4Example
• An engine transfers 2.00 x 10 3 J of energy from a hot reservoir during a cycle and transfers 1.50 x 10 3 J as exhaust to a cold reservoir
(A) Find the efficiency of the engine
(B) How much work does this engine do in one cycle?
J 10 5
0 )
10 5
1 ( )
10 2
( Q
Q '
W
%
25 10
2
10 5
.
1 1
Q
Q 1
e
3 3
3
' c h
3
3
h
' c
Trang 5The Carnot Engine
• The engine operates in a cyclic process consisting of 2 isothermal processes and 2 adiabatic processes
) V
V ln(
T
) V
V ln(
T 1 Q
' Q 1
e
) V
V ln(
nRT Q
'
Q
) V
V ln(
nRT Q
Q
0 Q
: adiabatic
:
DA
0
) V
V ln(
nRT Q
: isothermal
:
CD
0 Q
: adiabatic
:
BC
0
) V
V ln(
nRT Q
: isothermal
:
AB
A
B h
D
C c
h c
D
C c
CD c
A
B h
AB h
DA
C
D c
CD BC
A
B h
AB
received heat System released Heat
Trang 6The Carnot Engine (cont.)
D
C A
B
1 D c
1 A h 1
1 C c
1 B h 1
A
B h
D
C c
h c
V
V
V
V
V T V
T const
TV : adiabatic
:
DA
V T V
T const
TV : adiabatic
:
BC
) V
V ln(
T
) V
V ln(
T 1 Q
' Q
1
e
h
c
T
T 1
e
Trang 7Carnot
Cycle
In process D -A , (Active
Fig 22.9d), the base of the
cylinder is replaced by a
nonconducting wall and the
gas is compressed
adiabatically
The temperature of the gas
increases to T h, and the
work done by the piston
on the gas is W DA
In process C S D (Active Fig 22.9c), the
gas is placed in thermal contact
with an energy reservoir at temperature T c
and is compressed isothermally
at temperature Tc
During this time, the gas expels energy
|Qc| to the reservoir and the work done by the piston on the gas is W CD
Process A B is an isothermal expansion at temperature T h The gas is placed in thermal contact with an energy reservoir at
temperature T h During the expansion, the gas absorbs
energy |Q h| from the reservoir through the base of the cylinder
and does work W AB in raising the
piston
In process B C (Active Fig 22.9b), the
base of the cylinder is replaced by a thermally nonconducting wall and the gas expands adiabatically; that is, no energy enters or leaves the system by heat During the expansion, the temperature of the gas
decreases from T h to T c and the gas does
work W BC
in raising the piston
Trang 8Heat Pumps and Refrigerators
In a refrigerator or a heat
pump, the engine takes in
energy |Q c | from a cold
reservoir and expels energy
|Q h | to a hot reservoir (Active
Fig 22.4), which can be
accomplished only if work is
done on the engine
Trang 9Refrigerator
c h
c
c h
c
T T
T )
e mod cooling
( COP :
cycle _
Carnot
Q '
Q
Q )
e mod cooling
( COP
c h
c h
c h
c
Q '
Q Q
Q W
0 W Q
Q
U
W
Q or
refrigerat _
the _ on _ done _
Work
reservoir _
cold _
from _
received _
heat )
e mod cooling
(
COP
The effectiveness of a heat pump /refrigerators is described in terms of a
number called the coefficient of performance
Trang 10Heat Pump
c h
h
c h
h
c h
c h
c h
h
T T
T )
e mod heating
( COP :
cycle _
Carnot
Q '
Q
'
Q )
e mod heating
(
COP
Q '
Q Q
Q W
0 W
Q Q
U
W
' Q heatpump
_ the _
on _ done _
Work
reservoir _
hot _
to _ delivered _
heat )
e mod heating
(
COP
Trang 11SUMMARY
c h
c
c
Q '
Q
Q W
Q )
e mod cooling
( COP frigerator
Re
c h
c h
h h
Q '
Q
W
Q '
Q
'
Q W
'
Q )
e mod heating
( COP pump
Heat
h
' c h
' c h
Q 1
Q
Q
Q Q
'
W e
efficiency engine
Trang 12Example 22.5 Efficiency of the Otto Cycle
Find the thermal efficiency of an engine operating in an idealized Otto cycle Treat the working substance as an ideal gas
1 1
2 h
c
A D
B C
D
C A
B 1
2
1
1
1 2 C
1 1
D
1
1 2 B
1 1
A
C
A D
h c
A D
V DA
c
B C
V BC
h
D A
V DA
CD
B C
V BC
AB
V
V 1
Q
' Q 1
e
T T
T T
T
T T
T V
V
V T V
T
const TV
: adiabatic
:
CD
V T V
T
const TV
: adiabatic
:
AB
T T
T T
1 Q
' Q 1
e
) T T
( nC Q
'
Q
) T T
( nC Q
Q
0 ) T T
( nC Q
: ric isovolumet
:
DA
0 Q
: adiabatic
:
CD
0 ) T T
( nC Q
: ric isovolumet
:
BC
0 Q
: adiabatic
:
AB