4.2. Efficiency
A conversion of energy without loss is not possible. For
example, the electrical energy fed to a motor is converted not only into
mechanical energy but also in heat due to the rise in temperature of the motor.
Since this heating is not desired, this portion of the fed electrical energy
which is converted into heat energy is called energy loss or lost energy. The
efficienca is defined as the ratio of the energy delivered by the device to the
energy supplied to it.
h =
W_{e}/W_{i} = (P_{e} ·
t)/(P_{i} · t) =
P_{e}/P_{i}
(4.4.)
where:
h ^{1)} |
efficiency |
W_{e} |
effective energy (energy delivered) |
W_{1} |
indicated energy (energy supplied) |
P_{e} |
effective power |
P_{i} |
indicated power |
Since the delivered energy is always smaller by the lost energy
than the supplied energy, the efficiency is always smaller than 1. According to
equation (4.4,), the same statement applies to power. When the losses are small,
the efficiency will have a high value. The developmental level of a device is
substantially determined by the magnit de of the efficiency. Great efforts are
made to further improve the efficiency in order to convert the supplied energy
into the desired energy with losses a small as possible.
Table 4.2. shows a few typical examples of the values involved.
Table 4.2. Efficiency of Selected Technical Equipment
Equipment |
mean efficiency |
incandescent lamp |
0.05 |
steam locomotive |
0.2 |
small electric motor |
0.5 |
large electric motor |
0.85 |
transformer |
0.95 |
power station generator |
0.98 |
^{1)} h
Greek letter eta
In many cases, several devices having a certain efficiency each
are connected together and then the total efficiency of the arrangement is of
interest. Fig. 4.1. shows an example. The arrangement shown may be, for example,
a motor generator where device A is the electric motor, which takes up
P_{supplied 1} as electrical power and delivers P_{delivered 1}
as mechanical power. At the same time P_{delivered 1} is the drive power
supplied to the generator (device B) designated as P_{supplied 2}. The
power delivered by the generator is designated as P_{delivered 2}. The
motor has the efficiency h_{1} and the
generator the efficiency h2. The total
efficiency is expressed as
h =
P_{del2}/P_{supp1}
Fig. 4.1. Interaction of two
technical devices
P = P_{zu}; P = P_{ab}
When inverting the relation
h_{2} =
P_{del2}/P_{supp2 }for P_{supp2 }and h_{1} = P_{del1}/P_{supp1} for
P_{supp1}, we obtain
P_{del2} = h_{2}
· P_{supp2} and
P_{supp1} = P_{del1}/h_{1}
Substituted into the initial equation we obtain
h = (h_{2} ·
P_{supp2} · h_{1})/P_{del1}
Since, however, P_{del1 }= P_{supp2}, it follows
that
h = h_{1} · h_{2}
(4.5)
This shows that the total efficiency is equal to the product of
the individual efficiencies and, thus, always smaller than the smallest
individual efficiency.
Example 4.4.
The motor of a motor generator has an efficiency of 0.8 and the
generator an efficiency of 0.75. What is the total efficiency?
Given:
h_{1} =
0.8
h_{2} = 0.75
To be found:
h
Solution:
h = h_{1} · h_{2}
h =
0.8 · 0.75
h
= 0.6
The total efficiency is 0.6.
In any energy conversion process, losses occur. This
fact is described, by the efficiency. The conversion losses should be as small
as possible; this is expressed by a value of the efficiency near 1. The
efficienca is always smaller than 1. The total efficiency is the product of the
individual efficiencies.
Questions and problems:
1. Why calls technical progress for an increase in
the efficiency?
2. Give proof of the fact that for three devices connected
together the total efficiency is: = h_{1} · h_{2} · h_{3}.
3. A motor delivers a mechanical power of 650 W. What is its
efficiency when the current input is 3.5 A at a voltage of 220 V?
4. A motor generator has an input of 3 A while connected to a
voltage of 220 V and delivers a voltage of 48 V to the generator. The motor has
an efficiency of 0.8 and the generator of 0.78. What is the current drawn from
the
generator?