Environmental Engineering Reference
In-Depth Information
2.2.3 S ECOND L AW OF T HERMODYNAMICS
The second law of thermodynamics is derived from the principles of heat engines
first studied by Sadi Carnot. This can be best explained with reference to Figure 2.1,
in which a heat engine converts heat to work. The heat engine absorbs heat Q 1 from
the hot reservoir (heat source) at temperature T hot , converts part of it to work W , and
discards heat Q 2 to the cold reservoir (sink) at temperature T cold .The efficiency
η eff =
W/Q 1 . By the first law, W
=
Q 1
Q 2 , further, Q
T . Therefore, the efficiency of
a Carnot heat engine is given by
Q 1
Q 2
T hot
T cold
T hot
η eff =
=
.
(2.6)
Q 1
From the generalizations of the concept of efficiency of heat engines for an arbitrary
cycle, Carnot defined the following for a closed cycle:
d Q
T =
0,
(2.7)
where the integral is over a path representing a reversible process from state A to
state B. Thus, Carnot realized that the function d Q/T is independent of the path
and depends only on the initial and final states. Such a function was given the name
entropy, S :
d Q
T .
d S
=
(2.8)
The second law of thermodynamics is a general statement regarding the sponta-
neous changes that are possible for a system. When a change occurs in an isolated
system (i.e., the universe) the total energy remains constant; however, the energy may
be distributed within the system in any possible manner. For all natural processes
occurring within the universe, any spontaneous change leads to a chaotic dispersal
of the total energy. It is unlikely that a chaotically distributed energy will in time
reorganize itself into the original ordered state. A large number of examples can be
Hot
Cold
Q 2
Q 1
T cold
T hot
W
FIGURE 2.1 A Carnot heat engine.
 
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