Page 34 - Low Temperature Energy Systems with Applications of Renewable Energy

Principles and operation of refrigeration and heat pump systems 23

the Second Law of thermodynamics which places limits on the performance of a sys-
tem. Once the maximum allowable performance is known, actual systems may then be
compared to this ideal and deficiencies identified for improvement.
The following equations are used to carry out an exergy analysis of any thermody-
namic system. Imagine a general system interacting with its surrounding in several
ways: work and heat transfer may occur, and mass may flow in or out of the system
at various point on the surface. Each of these carries not only energy but also exergy,
e,defined as

e i h h i h 0 T 0 ðs i s 0 Þ (1.16)

where h i and s i are the enthalpy and entropy of the material flowing at each inlet or
outlet, T 0 is the absolute temperature of the surroundings (dead state), and the subscript
0 refers to the dead state conditions. The dead state properties are evaluated at T 0 and
P 0 . The specific exergy in Eq. (1.16) when multiplied by the mass flow rate yields the
rate of exergy or exergetic power

_
E i ¼ _ m i e i (1.17)
_
_
If heat transfer Q is involved, the exergy E Q associated with the heat is given by:

_ T 0 _
E Q ¼ 1 Q (1.18)
T
where the factor in brackets is the Carnot efficiency for an ideal power cycle operating
between T and T 0 ; see Eq. (1.1). Thus the exergy associated with a heat transfer is the
maximum amount of work that ideally could be produced from it by a cycle operating
as a Carnot cycle.
_
If work transfer is involved, the exergy associated with that work transfer E W is
exactly the amount of work delivered, undiminished by any irreversibility such as fric-
tion. Thus,
_
E W ¼ W _ (1.19)

The exergy accounting for a heat pump operating as a steady system will involve
the exergy associated with each flow stream and each exergy transfer term. Unlike a
First Law energy balance in which energy is conserved, an exergy accounting will al-
ways show that less exergy leaves the system than enters it. That is, some exergy will
always be destroyed. If one imagines a perfect world where all dissipative phenomena
could be eliminated and all processes were carried out reversibly, then no exergy
would be lost; unfortunately this is not possible in the real world. The objective of
_
an exergy analysis is to identify the lost or destroyed exergy DE i and devise ways
to reduce those losses [19,20].