Modern Engineering Thermodynamics

340 CHAPTER 10: Availability Analysis
3. Those whose primary function involves energy transfers internal to the system (such as heat exchangers).
4. All other technologies.
For example, given a technology whose primary function is energy output, we can write
Actual useful energy output = Maximum reversible useful energy output − Lost energy
and, given a technology with a primary function of absorbing energy, we have
Actual useful energy input = Maximum reversible useful energy input + Lost energy
where we recognize that, in each case, the lost energy is not destroyed but only in a form not used by the technology.
A different and more revealing type of energy conversion efficiency can now be defined, based on ratios of available
energy rather than total energy. This new efficiency contains terms representing the irreversibilities within the system,
so that we can see exactly where the loss of efficiency occurs within a system. To distinguish it from the ordinary first
law efficiencies already discussed, this new type of energy conversion efficiency is given the symbol ε and is called
second law efficiency.
10.11.2 Second Law (Availability) Efficiency
Of the available energy initially resident in (or the net available energy put into) a system, some of it leaves the
system with the “desired result” of the operation of the system, some of it is lost to the local environment
(usually through unwanted heat transfer), and some of it is destroyed by the irreversibilities operating inside the
system. This can be written in equation form as
A initial or = A desired + A loss + A destruction (10.28)
net input result
We can now define a meaningful second law efficiency (or effectiveness) ε based on availability as
Second law efficiency
ε =
A desired
result
A initial or
net input
=
_A desired
result
_A initial or
net input
(10.29)
EXAMPLE 10.10
Determine the first and second law efficiencies for heating a liquid from
temperature T to temperature T + ΔT in a closed, uninsulated tank. The temperature
change ΔT is due to an external heat transfer Q in , and since the tank
is not insulated, there is also a heat loss to the local environment, Q loss . The
ground state temperature is T 0 .
Solution
First, draw a sketch of the system (Figure 10.15).
T
Q in
T +ΔT
The unknowns are the first and second law efficiencies for heating a liquid from
temperature T to temperature T + ΔT in a closed, uninsulated tank.
An energy balance for this system with W = 0 and Δpe = Δke = 0is
Ground state:
Temperature = T 0
Q loss
Q in − jQ loss j − 0 = mu ð 2 − u 1 + 0 + 0Þ
or
Q in = mu ð 2 − u 1 Þ+ jQ loss j
For an incompressible liquid, we can write
u 2 − u 1 = cðT 2 − T 1 Þ = c½ðT + ΔTÞ − TŠ = cðΔTÞ
FIGURE 10.15
Example 10.10.
The “desirable result” here is the increase in internal energy of the liquid in the tank, m(u 2 − u 1 ), so the first law (thermal)
efficiency is
η T =
Desirable result
Cost
= mðu 2 − u 1 Þ
Q in
mc ΔT
= ð Þ
Q in