Carnot Cycle
Examples of the Carnot cycle
French engineers like Carnot were very interested in designing engines that efficiently burned coal
in order to do work. These “heat engines” were the basis of the European and later the American
Industrial evolution. Carnot imagined and idealized form of the “heat engine” that is particularly
useful to help us imagine how the atmosphere behaves as a heat engine.
In the atmosphere, we can easily think of the sun heating the Earth. This lowers the air’s
density, and then the heated airmass does work by expanding upwards or outwards. Meanwhile it
radiatively cools to space, and then it contracts
Figure 1: Carnot cycle: heating does positive expansion work at constant temperature; cooling
does negative contraction work; in between there is adiabatic expansion and compression.
Efficiency
Since true changes in the atmosphere are always irreversible, it is more accurate to say
T ds (universe) > du (system) + pda (system)
which, is equivalent to saying that, if the state of the system doesn’t change (du = 0), the second
law says you must always put more heat T ds into a system than the amount of pda work you
1
Adiabat
B
C
Temperature, T
T1
T2
A
D
Isotherm
Isotherm
es
es – des
B
A
Volume
(a)
C
D
Saturated vapor pressure
Adiabat
Saturated vapor pressure
resent equal net work done by or on the working
substance are particularly useful. The skew T ! ln p
chart has this property.
es
es – des
A, D
T – dT
Temperature
(b)
Fig. 3.23 Representation on (a) a saturated vapor pr
versus volume diagram and on (b) a saturated vapor pr
X
Y
versus temperature diagram of the states of a mixtur
Entropy, S
liquid and its saturated vapor taken through a Carnot
Fig. 3.22 Representation of the Carnot cycle on a temperaBecause the saturated vapor pressure is constant if tem
Figure 2: The Carnot Cycle in S-T space, from Wallace and Hobbs. Note that A in Figure 1
ture (T)–entropy (S) diagram. AB and CD are adiabats, and
ture is constant, the isothermal transformations BC an
corresponds with B above.
BC and DA are isotherms.
are horizontal lines.
40
get out of it - the efficiency of any process must be less than 100%. We define the efficiency of
a process as the ratio of working to heating. What percentage of energy added to a system gets
The temperature–entropy diagram was introduced into meteorology by Shaw.41 Because entropy is sometimes represented
converted to useful work? If the state of the system doesn’t change so that Du = 0, then
symbol " (rather than S), the temperature–entropy diagram is sometimes referred to as a tephigram.
R t da Lecturer
41 Sir (William) Napier Shaw (1854–1945) English meteorologist.
in Experimental Physics, Cambridge University, 1877
0
Dw
0 p dt 0 dt
Director of the British Meteorological Office, 1905–1920.
Meteorology,
Imperial College, University of London, 1920
h⌘
=Professor
1
R t dq of <
0
Dq
Shaw did much to establish the scientific basis of meteorology.
interests ranged from the atmospheric general circulation and fo
0His
dt 0 dt
ing to air pollution.
But the
first law says that energy must be conserved, i.e. we don’t lose it. So what happens if
42 Benoit
Paul Emile Clapeyron (1799–1864) French engineer and scientist. Carnot’s theory of heat engines was virtually un
heating
isn’t
converted
to working?
It isThis
lostbrought
as waste
heat. Thus,
canattention
imagineofa cycle
where
until Clapeyron expressed
it in analytical
terms.
Carnot’s
ideas one
to the
William
Thomson (Lord Kelvi
Clausius, who utilized them in formulating the second law of thermodynamics.
Dw = Dqin
implying that
h=
Dqout
Dqin Dqout
Dqin
You eat food to do work, and the rest of the energy gets lost as heat. The Earth gets heated by the
sun, and it uses this Dqin energy to do work in the form of atmospheric motions, with the remainder
of the energy Dqout getting lost to space through thermal radiation at the top of the atmosphere.
The efficiency in this case is about 1 to 2%. In other words, only a tiny fraction of solar energy
goes into creating atmospheric motions.
2
800–
900–
1
5
5
-5
-5
0
10
10
0
5
5
0
-5
1000–
800–
900–
1
0
-5
1000–
Figure 3: The Carnot Cycle on a Skew-T.
Figure 4: The Carnot Cycle in a Hurricane.
3