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
We	effective energy (energy delivered)
W1	indicated energy (energy supplied)
Pe	effective power
Pi	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 h₁ 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

h₂ = P_del2/P_supp2 for P_supp2 and h₁ = P_del1/P_supp1 for P_supp1, we obtain

P_del2 = h₂ · P_supp2 and

P_supp1 = P_del1/h₁

Substituted into the initial equation we obtain

h = (h₂ · P_supp2 · h₁)/P_del1

Since, however, P_del1 = P_supp2, it follows that

h = h₁ · h₂

(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:

h₁ = 0.8
h₂ = 0.75

To be found:

h

Solution:

h = h₁ · h₂
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: = h₁ · h₂ · h₃.

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?