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Rational Efficiency
of
a
Powerplant
4.1 The influence of fuel properties on thermal efficiency
The thermal efficiency of a cycle has been defined previously, in terms of specific
quantities, as
w,t
9th
=

qin
where
wnet
=
net work output from the cycle per unit mass of fluid,
and
=
energy addition to the cycle per unit mass of fluid.
In this case
is the energy transfer to the working fluid, and does not take into account
any losses in the boiler or heat transfer device. Equation (4.1) can be rewritten for the
whole powerplant, including the boiler or heat transfer mechanism, as
(4.2)
W",t
%'qBVth=

Ah0
where
l;lo
=
overall efficiency of powerplant,
l;lB
=
efficiency of boiler,
qth
=
thermal efficiency of cycle,
wWt
=
net work output from the cycle
per
unit
mass
of fuel,
Ah,,
=
specific enthalpy of reaction of fuel.
This might be considered to be an unfair, and possibly misleading, method of defining
the efficiency because the energy addition cannot all be turned into work, as was shown
when considering exergy and availability. Another definition of efficiency can be derived
based on the Second Law, and this relates the work output from the cycle to the maximum
work output obtainable.
The efficiency of the powerplant has been related, in eqn (4.2), to the amount of energy
that has been added to the cycle by the combustion of the fuel. In the past this has been
based on the enthalpy of reaction of the fuel, or usually its calorific value,
Qi. It
was
shown previously (Chapter 2) that this is not the energy available for the production of
work, and that the maximum available work that can be obtained from the fuel is based on
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View Full Document Rational efficiency
65
the change of its
exergy
at the dead state conditions. Hence, the maximum available work
from unit mass
of
fuel
is
Ago
=
g,

Ago
=
Ah0

To(s,

SPo>
(4.3)
This is related to the enthalpy of formation by the equation
(4.4)
It was shown in Chapter 2 that
I
I
could be greater than or less than
I
Aho
1
,
and the
difference was dependent on the structure of the fuel and the composition of the exhaust
products. The efficiency of the powerplant can then be redefined as
(4.5)
Wnet
a=
where
wmt
=
actual net work output from the cycle
per unit mass of fuel,

Ago
and
=
change of Gibbs function caused by combustion,
=
maximum net work obtainable from unit mass of fuel.
Equation (4.5) 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 function instead of the
enthalpy of reaction is usually small (a few per cent).
4.2 Rational efficiency
When the efficiencies defined in eqns (4.2) and (4.5) 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 4.1). For
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This note was uploaded on 03/09/2010 for the course MECHANICAL ME9802701 taught by Professor Prof.william during the Spring '10 term at Institut Teknologi Bandung.
 Spring '10
 Prof.William

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