Environmental Engineering Reference
In-Depth Information
In this form, the first law expresses the finite change in energy of the system as equal to the sum of
the heat transferred to the system minus the work done by the system on the environment during
the process that brought about the change from the initial to the final state.
The integrals of the heat and work quantities on the right-hand side of the equation (3.8) cannot
be evaluated unless the details of the process that caused the change from the initial to the final
state of the system is known. In fact, there may be many different processes that can bring about the
same change in energy of the system, each distinguished by different amounts of heat and work,
but all having in common that the sum of the heat and work quantities added to the environment
are the same for all such processes that change the system from the same initial to final states.
In some power-producing and refrigeration systems, a working fluid undergoes a series of
heating, cooling, and work processes that returns the fluid to its initial state. Because
E
f
=
E
i
for
such a cyclic process, the integral expression of the first law of thermodynamics, equation (3.8),
has the form
d
Q
=
d
W
(3.9)
where the symbol
identifies the cyclic process for which the heat and work integrals are evaluated.
In other words, in a cyclic process the net heat and work quantities are equal.
3.5
THE SECOND LAW OF THERMODYNAMICS
The goal of engineers who design power plants is to devise a system to convert the energy of a fuel
into useful work. If we consider the combustion of a fossil fuel to provide a source of heating, then
the desirable objective is to convert all of the fuel energy to work, as the first law, equation (3.9),
allows. However, the second law of thermodynamics states that it is not possible to devise a cyclic
process in which heating supplied from a single source is converted entirely to work. Instead, only
some of the heat may be converted to work; the remainder must be rejected to a heat sink at a lower
temperature than the heat source. In that way the net of the heat added and subtracted in the cycle
equals the work done, as the first law requires.
It is not possible to express directly this second law statement in the form of an equation.
However, it is possible to deduce three important consequences of the second law. The first is that
there exists an absolute temperature scale, denoted by
T
, which is independent of the physical
properties of any substance and which has only positive values. The second is that there is a
thermodynamic property called entropy, denoted by
S
, whose incremental change is equal to the
heat interaction quantity
d
divided by the system temperature
T
for any incremental process in
which the system temperature remains spatially uniform, called a reversible heat addition, or
Q
d
T
dS
≡
(3.10)
re
v
The third deduction is called the inequality of Clausius. It states that, in any process,
dS
is equal
to or greater than the ratio
d
Q/
T
,
d
T
dS
≥
(3.11)
