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Efficiency in Physics

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Imagine today you have to do a physics project. Maybe, the project is a little bit difficult but you understand the subject well and only use a couple of hours to complete it. The next morning you ask your colleague and he tells you he was doing the project for five hours. Your physics teacher hears you and says that you have been more efficient than your colleague, as you needed fewer resources than your colleague to achieve the same result.

This is the way that the term efficiency is usually used, but there is a slightly more technical definition that is used in physics.

When we talk about efficiency in physics, we are referring to the ratio of the useful energy output of a system to the total input energy transferred to that system.

Just to remember, in physics energy is defined as the property of a system that allows it to perform work and cause some change in the motion of an object or to heat it. We can distinguish between different types of energy, such as mechanical energy (related to movement), thermal energy (related to temperature), sound energy, kinetic energy, electric energy, etc.

The efficiency rating of an electrical appliance can be a useful and quick way of judging its efficiency accurately, adapted from image by Loominade CC BY-SA 4.0

To understand the concept of efficiency it is important to understand the law of conservation of energy. This law states that energy is neither created nor destroyed. Instead, it is transferred from one form to another in different ways. When we talk about efficiency we refer to the difference between the energy put into the system and the useful energy obtained out of the system, which will always lower than the total input energy. This difference is why we have an energy loss. But as the law of the conservation of energy states, that energy is not destroyed. This energy is transformed into other types of energy such as thermal energy, increasing the system's temperature or sound energy, producing a sound that we can hear.

It is important to understand the difference between efficiency and effectiveness. Being efficient means obtaining the result desired with the minimum energy loss as a ratio of the total input energy. On the other hand, effectiveness is how likely we are to obtain the desired result, no matter how many resources are used or wasted in the process. For example, using animals to plough fields can be effective, but it is not very energy efficient because a lot of energy is required to grow the crops that are used to feed the animals, and a lot of energy is wasted in the digestion of the food, the growth, and maintenance of the animal, growing inedible parts of crops etc.

Imagine we have a car which we fill with oil. That oil is converted into energy by the system thanks to the engine of the car. But, when we start the car, we can see the engine increases its temperature, it starts making a sound, etc. Therefore, all of the energy we have "introduced" in the form of oil (the generates useful work by combusting this oil) would not completely be converted into a car's movement.

We can compute the efficiency of this car to see what percentage of the energy introduced is transformed into the mechanical energy we desire. That will tell us how efficient the car is. Remember this has nothing to do with the effectiveness of the car. As long as the car achieves its goal (transport the people from one point to another), it will be effective.

Competition cars try to be as efficient as possible because it is an important characteristic to be competitive, adapted from image by Angmokio CC BY 2.5

Efficiency formula and symbol

Now we understand what efficiency in physics is. But we need a way to compute it, right? Generally, we can express the efficiency as:

The efficiency can also be represented with the symbol. It is easy to see that the efficiency does not have units, as it is the ratio of two variables with the same units. This efficiency has to be, at maximum, equal to one and always greater than or equal to zero. In a non-ideal process, it is lower than one. If we want to express this efficiency as a percentage we simply multiply it by 100:

We can also express the efficiency in terms of the total input and useful output power, which is the rate of change of energy transfer and can be expressed as:

or in words,

Therefore, if we know the income power of a system or a machine and its outcome power, we can compute the efficiency in the following way:

In a non-ideal case, the income of energy has to be greater than the outcome energy. Therefore, we can express this difference as:

Whererefers to the energy that is lost in the process into other types of energy. There are more ways to compute the efficiency of a system regarding the energy involved in the process which we will see in the next topic with some examples.

Efficiency calculation

Let’s compute an easy exercise to see how we would compute the efficiency of a machine. Imagine an engine that takesminutes to perform a process (such as moving a car, or bumping water) that requires an energy of. This engine consumes (theoretically). Which is the efficiency of this machine?

Firstly, we would have to compute the power involved in the process mentioned. As we have seen previously, to compute the power (remember that we express the time in seconds):

Now we just have to compute the efficiency η with the formulas we have learned. Remember that the power involved in the process will be(outcome) and the theoretically consumed by the machine will be(income):

So, the machine has an efficiency of(to compute the percentage we just multiply the efficiency by)

Examples of efficiency in physics

Along with the article, we have discussed how energy can take different forms and compute the efficiency for these different types of energy. Now let’s see some examples of these energies and see how to use the formula of the efficiency to compute the efficiency in these cases.

Mechanical efficiency

In this case, a machine performs work that consists of moving an object through a certain distance. Therefore, the income energy is used to perform that work, which will be the resultant outcome energy. We use the previous formula to compute the efficiency.

The energy loss is produced by friction, which is a resistance force to the movement so the energy will dissipate in the form of heat or sound. An example is a car, any other type of vehicle, or any other machine with a motor or moving parts.

Electrical efficiency

To compute the electrical efficiency we also use the formula we have seen before of the division between the income and the output power. We use this efficiency for some home appliances and light bulbs. There are some techniques to increase electrical efficiency as will be discussed later.

Thermal efficiency

We use thermal efficiency to compute the efficiency of heat engines, which are machines that transform heat energy into work, which is another type of energy. In a heat machine, we have two sources of heat at different temperatures, one at a larger temperature and the other at a lower temperature.

In the case described for the thermal efficiency where two sources have different temperatures, the efficiency can be computed as:

Whereis the heat that leaves the machine that transforms heat into work, andis the heat that enters.

In thermal machines, there is a limit to efficiency. That limit is established by Carnot's theorem. This theorem states that the maximum efficiency of a thermal machine is given by the temperatures of the sources.

is the temperature of the hottest source andis the temperature of the coldest one. No matter the adjustments to avoid energy losses such as friction, the efficiency would not be higher than this one.

Carnot heat engine, commons.wikimedia.org

Increasing efficiency in physics

Increasing efficiency is one of the main goals when we use energy and transfer it. That is why it is so important to find ways to minimize energy loss.

For example, as we have seen, when we transform any kind of energy into mechanical energy, some percentage of this energy is lost due to friction. There are some ways to reduce this energy loss:

• The force of friction, and therefore the energy loss, is directly proportional to the coefficient of friction, which is particular to each surface. Using surfaces with a lower friction coefficient or using lubrication can help to reduce energy loss.
• When the object is moving, using wheels can help to reduce the effects of friction. Also, we can try to reduce the resistance produced by the air by moving more slowly or using streamlined designs, where the air resistance effect is lower because of how it flows.

Improving electrical efficiency is also essential nowadays. The main way we achieve this when transporting electricity from one point to another over long distances is by reducing the current and increasing the voltage for a given power in power lines. This way the electricity can travel faster and the energetic losses are reduced to two percent approximately. Once electricity has arrived at zones with population, the power is reduced.

Power lines where the voltage is increased in order to maximize efficiency, commons.wikimedia.org

Also, we could use superconductors to reduce energy losses. These superconductors are made of materials that allow electricity to pass through them without getting heated and with an energy loss of approximately zero due to their extremely low electrical resistance. The problem with these kinds of superconducting materials is that they are very expensive to maintain so their use is not currently economically viable.

Efficiency in Physics - Key takeaways

• Efficiency is the ratio of the useful energy output of a system to the total input energy.
• Energy can be transformed from different types into others such as thermal energy, mechanical energy, light energy etc.
• The law of the conservation of energy states that energy is neither created nor destroyed, but rather it is transformed from one form to another. Therefore, there is an energy loss in a process that is transformed into another type of energy. Normally that energy loss is produced by friction.
• There is a direct relationship between the energy loss of a process and the efficiency of the machine that performs it.
• Effectiveness is the degree of success of a result desired, no matter the resources used. A machine can be effective but not efficient.
• To compute the efficiency we divide the outcome energy by the income energy. It works the same for the power.
• Efficiency can be increased in many ways. For mechanical efficiency, we can use lubrication and wheels. Also, electrical efficiency can be increased with techniques regarding the modification of the power or superconductors.

In physics, efficiency is the ratio of the useful energy of a system to the total input in that system.

You can find examples of efficiency in your domestic devices. These devices are normally categorized depending on how efficient they are. If they have an efficiency of "A" it means they are very efficient, and therefore they would not waste much energy while performing their function.

Generally, the formula for calculating the efficiency is:

efficiency = (useful output energy transfer) / (total input energy transfer)

Efficiency is used to identify which devices have smaller energetic losses. Therefore, it helps us to choose devices that will perform an amount of work with smaller energy input, helping us to save energy.

The symbol for efficiency in physics is the Greek symbol Eta  -  η

Final Efficiency in Physics Quiz

Question

What is meant by efficiency in physics?

Efficiency is the ratio of the useful energy of a system to the total input in that system.

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Question

The law of the conservation of energy states that...

energy is neither created nor destroyed, it is transferred into different forms or types.

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Question

Is effectiveness a synonym for efficiency?

No, effectiveness is the degree of accomplishment of the desired result.

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Question

Which of these is not a type of energy?

Thermal energy.

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Question

Which units does efficiency have (standard unit)?

None.

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Question

How does an energy loss happen during a process?

There is an energy loss during a process when a part of the energy input is transformed into other types of energy different from the useful energy output. For example, when an engine gets heated, this thermal energy is an energy loss.

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Question

How can we increase mechanical energy when moving an object?

All of them are true.

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Question

If the electricity is transported over long distances, what happens when the current is reduced and the voltage for a given power is increased in power lines?

The electricity will travel faster and the energetic losses are reduced.

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