Environmental Engineering Reference
In-Depth Information
heat engine is the difference between the heat charged (
Q
1
) and the heat discharged
(
Q
2
);
W
=
Q
1
-
Q
2
. Therefore, the efficiency of the heat engine is equal to (
Q
1
−
Q
2
)/
Q
1
.
The maximum value of the thermal energy that can be taken in and out during the
operation of the heat engine is proportional to the temperature at each stage, so the
maximum value of efficiency (
η
) can also be written as
η
max
= (
T
1
−
T
2
)/
T
1
This is called the Carnot efficiency, and the efficiency of any heat engine cannot
in principle exceed the Carnot efficiency.
Efficiency of a Fuel Cell
In contrast to the heat engine, the fuel in a fuel cell is con-
verted, without burning, directly into electricity, so the power generation in a fuel
cell is not restricted by the Carnot efficiency. The maximum value of the efficiency
of the fuel cell is Δ
r
G
/Δ
r
H
as shown above, but in reality (Fig.
4.4
), when taking out
electrical current, this causes a voltage loss due to internal resistance, and the effi-
ciency decreases. Accordingly, the real fuel cell efficiency is best considered with
reference to the operating voltage. If the fuel cell is operated at
V
out
, and as a result
of the reaction of 1 mol oxygen atom, an electric current of 2
F
1
coulomb flows in
the external circuit, an energy of 4
FV
out
joule is retrieved. If the ratio of the fuel flow
used for the electrochemical reaction is
f
, then we can express the efficiency of a cell
or a stack by the following formula.
η
=
2
FfV
∆
H
out
r
When a fuel cell is integrated into a system, further sources of efficiency loss should
be taken into consideration. Since the fuel cell generates direct current (DC), it may
be converted to alternating current (AC) using an inverter, which causes an effi-
ciency loss of 5-10 %. The auxiliary equipment for water circulation and air blower
etc. will also consume power. The system efficiency is thus calculated as an overall
efficiency of the fuel to the electricity output.
Comparing the Efficiency of Actual Systems
Heat engines can range from a rela-
tively small gas engine system of just a few kW to a few MW class, to a large-scale
power station where gas and/or steam turbines are used. Given the aforementioned
Carnot efficiency, the efficiency increases as the operating temperature
T
1
becomes
higher. Modern gas turbines burn the fuel at high temperatures exceeding 1500 °C.
In addition, some combine with a steam turbine using the exhaust heat to make
a 'combined cycle', which can reach a 60 % LHV efficiency. However, with the
heat engine, as shown in Fig.
4.5
, obtaining a high efficiency is difficult for small
systems.
On the other hand, the fuel cell, unlike the heat engine, has less of a size-effect
on power generation efficiency. An efficiency of ~ 50 % LHV can be achieved not
only with 100 kW class systems but also with 1 kW class residential fuel cell sys-
tems. Some recently announced systems show efficiencies exceeding 60 % LHV. In
contrast to heat engines, the larger the system becomes, the more fluid and thermal
management becomes difficult. Development is underway for fuel cell-gas turbine-
1
F
is the Faraday Constant, 96485 C/mol.
