Efficiency in Physics

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.

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.

Competition cars try to be as efficient as possible because it is an important characteristic to be competitive.

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 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:

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.

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.

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.