Page 114 - Advanced thermodynamics for engineers

100 CHAPTER 5 RATIONAL EFFICIENCY OF POWER PLANT

obtained from the fuel is based on the change of its exergy at the dead-state conditions. Hence, the
maximum available work from unit mass of fuel is

(5.3)
Dg 0 ¼ g R 0 g P 0
This is related to the enthalpy of formation by the equation

(5.4)
Dg 0 ¼ Dh 0 T 0 s R 0 s P 0
It was shown in Section 4.9.2 that jDg 0 j could be greater than, or less than, jDh 0 j, and the difference
was dependent on the structure of the fuel and the composition of the exhaust products. The efficiency
of the power plant can then be redefined as
u net
h ¼ (5.5)
0
Dg 0
where
u net ¼ actual net work output from the cycle per unit mass of fuel and
Dg 0 ¼ change of Gibbs energy caused by combustion
¼ maximum net work obtainable from unit mass of fuel.

Equation (5.5) is often referred to as the Second Law Efficiency, because the work output is related to
the available energy in the fuel, rather than its enthalpy change. The actual effect on thermal efficiency of
using the change of Gibbs energy instead of the enthalpy of reaction is usually small (a few percent).

5.2 RATIONAL EFFICIENCY
When the efficiencies defined in Eqns (5.2) and (5.5) are evaluated they contain terms which relate to
the ‘efficiency’ of the energy transfer device (boiler) in transferring energy from the combustion gases
to the working fluid. These effects are usually neglected when considering cycles, and the energy
added is related to the change in enthalpy of the working fluid as it passes through the boiler,
superheater, etc. Actual engine cycles will be considered later. First, a general heat engine will be
considered, see Fig 5.1. For convenience, the values will all be taken as specific values per unit mass
flow of working fluid.
The engine shown in Fig 5.1 could be either a wholly reversible (i.e. internally and externally) one
or an irreversible one. If it were internally reversible then it would follow the Carnot cycle 1-2-3s-4-1.
If it were irreversible then it would follow the cycle 1-2-3-4-1. Consider first the reversible cycle. The
efficiency of this cycle is
0 0
w net ðT 1 T 3s Þðs 2 s 1 Þ ðT H T L Þðs 2 s 1 Þ
h ¼ ¼ ¼ (5.6)
th
0
q in T 1 ðs 2 s 1 Þ T H ðs 2 s 1 Þ
0
which is the efficiency of an internally reversible engine operating between the temperature limits T H
and T L . This efficiency will always be less than unity unless T L ¼ 0. However, the Second Law states
0
0
that it is never possible to convert the full energy content of the energy supplied into work, and the
maximum net work that can be achieved is
b w net ¼ b 2 b 1 ¼ h 2 h 1 T 0 ðs 2 s 1 Þ (5.7)
where T 0 is the temperature of the dead state.