Page 115 - Mechanical Engineers' Handbook (Volume 4)

104 Thermodynamics Fundamentals

˙
S ˙ ms ˙ ms Q
S ˙ gen i
t out in i T i
and is a measure of the irreversibility of open system operation. The engineering importance
˙
of S gen stems from its proportionality to the rate of destruction of available work. If the
˙
m
following parameters are fixed—all the mass flows ( ), the peripheral conditions (h, s, V,
Z), and the heat interactions (Q , T ) except (Q , T )—then one can use the first law and the
i
i
0
0
second law to show that the work-transfer rate cannot exceed a theoretical maximum. 1,3,4
W V 2 gZ Ts V 2 gZ T s (E Ts)

˙
˙ mh
˙ mh
in 2 0 out 2 0 t 0
˙
The right-hand side in this inequality is the maximum work transfer rate W sh,max , which would
exist only in the ideal limit of reversible operation. The rate of lost work, or the rate of
exergy (availability) destruction, is defined as
˙
˙
˙
W lost W max W
Again, using both laws, one can show that lost work is directly proportional to entropy
generation,
˙
W TS ˙
lost 0 gen
This result is known as the Gouy-Stodola theorem. 1,3,4 Conservation of useful work (exergy)
in thermodynamic systems can only be achieved based on the systematic minimization of
entropy generation in all the components of the system. Engineering applications of entropy
generation minimization as a design optimization philosophy may be found in Refs. 1, 3,
and 4, and in the next chapter.
6 RELATIONS AMONG THERMODYNAMIC PROPERTIES
The analytical forms of the first and second laws of thermodynamics contain properties such
as internal energy, enthalpy, and entropy, which cannot be measured directly. The values of
these properties are derived from measurements that can be carried out in the laboratory
(e.g., pressure, volume, temperature, specific heat); the formulas connecting the derived prop-
erties to the measurable properties are reviewed in this section. Consider an infinitesimal
change of state experienced by a closed system. If kinetic and gravitational energy changes
can be neglected, the first law reads
Q any path W any path dU

which emphasizes that dU is path-independent. In particular, for a reversible path (rev), the
same dU is given by
Q rev W rev dU

Note that from the second law for closed systems we have Q rev TdS. Reversibility
(or zero entropy generation) also requires internal mechanical equilibrium at every stage
during the process; hence, W rev PdV, as for a quasistatic change in volume. The infin-
itesimal change experienced by U is therefore
TdS PdV dU