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)