# Efficiency in Physics

Efficiency is an important concept in physics, as it helps us understand how much energy is used to do work versus how much is lost or wasted to the environment. In physics, efficiency is the ratio of the useful energy output of a system to the total input energy transferred to that system. This is different from effectiveness, which is how likely we are to obtain the desired result, no matter how many resources are used or wasted in the process.

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, but is instead transferred from one form to another in different ways. As a result, the useful energy output of a system will always be lower than the total input energy, resulting in an energy loss. 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.

The efficiency rating of an electrical appliance can be a useful and quick way of judging its efficiency accurately. For example, 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. We can compute the efficiency of this car to see what percentage of the energy introduced is transformed into the mechanical energy we desire. This will tell us how efficient the car is, which is different from the effectiveness of the car, which is how likely it is to achieve its goal.

## Efficiency formula and symbol

Efficiency is an important concept in physics that helps us understand how much energy is used to do work versus how much is lost or wasted to the environment. But how do we compute efficiency?

We can express efficiency as the ratio of useful output energy to total input energy. We can also express it in terms of total input and useful output power, which is the rate of change of energy transfer. If we know the input power and output power of a system, we can compute the efficiency by dividing useful output power by input power.

In a non-ideal case, the input energy has to be greater than the output energy, resulting in energy loss. We can express this difference as the amount of energy lost in the process into other forms, such as thermal or sound energy. There are various ways to compute efficiency of a system regarding the energy involved in the process, which we will explore in the next topic with some examples.

## Efficiency calculation

Let's try an exercise to see how we can compute the efficiency of a machine. Imagine an engine that takes 10 minutes to perform a process that requires an energy of 5000 joules. This engine consumes 2000 joules (theoretically). What is the efficiency of this machine?

First, we need to compute the power involved in the process using the formula we learned earlier, which is P = E/t. We need to express the time in seconds, so 10 minutes is 600 seconds. Therefore, the power involved in the process is:

P = 5000/600 = 8.33 J/s

Now, we can use the formulas to compute efficiency. The power output (or useful output) of the machine is 8.33 J/s, and the power input (or theoretically consumed) by the machine is 2000 J. Therefore, the efficiency can be calculated as:

η = (8.33/2000) x 100% = 0.4165%

So, the machine has an efficiency of 04165%, which is very low.

## Examples of efficiency in physics

Absolutely! Let's take a look at some examples of different types of energy and how we can use the efficiency formula to compute their efficiency.

- Electrical energy: Suppose we have an electric motor that converts electrical energy into mechanical energy to perform a task. If the motor consumes 1000 watts of electrical power and produces 800 watts of mechanical power, we can compute the efficiency as:

η = (800/1000) x 100% = 80%

- Thermal energy: Consider a boiler that generates steam to produce electricity. If the boiler consumes 5000 joules of fuel energy and produces 3000 joules of electrical energy, we can compute the efficiency as:

η = (3000/5000) x 100% = 60%

- Solar energy: Let's say we have a solar panel that converts sunlight into electrical energy. If the solar panel receives 1000 watts of sunlight and produces 100 watts of electrical power, we can compute the efficiency as:

η = (100/1000) x 100% = 10%

These are just a few examples of different types of energy and how we can compute their efficiency using the formula we learned earlier. It's worth noting that the efficiency of a system can be improved by minimizing energy loss and maximizing output energy

**Mechanical efficiency**

That's correct! In the case of a machine performing work by moving an object through a certain distance, the energy input (income) is used to perform the work, and the energy output (outcome) is the work performed. The efficiency can be calculated using the formula:

η = (work output/work input) x 100%

However, as you mentioned, energy loss occurs due to friction, which is a resistance force that opposes the motion of the object. This energy loss results in the dissipation of the energy in the form of heat or sound, reducing the efficiency of the machine.

In the case of a car or any other vehicle, the energy input is the fuel that is burned in the engine, and the energy output is the work done by the car, which is the movement of the car over a certain distance. The efficiency of the car can be improved by reducing frictional losses, such as using better lubrication, reducing air resistance, or using more efficient engines.

Overall, minimizing energy loss due to friction is an essential factor in improving the efficiency of machines and systems.

**Electrical efficiency**

The formula to calculate electrical efficiency is the same as the one we used earlier, which is:

η = (output power/input power) x 100%

This formula is used to calculate the efficiency of home appliances and light bulbs, which convert electrical energy into light, heat or mechanical energy.

In order to increase the electrical efficiency, there are several techniques that can be used. One technique is to use energy-efficient appliances and light bulbs, which are designed to consume less energy while producing the same amount of output. Another technique is to improve the insulation of homes and buildings, which reduces the amount of energy required for heating and cooling.

In addition, using renewable energy sources such as solar or wind power can significantly increase the electrical efficiency of homes and buildings, as these sources of energy are more sustainable and produce less pollution than traditional fossil fuels.

Overall, increasing electrical efficiency is an important step towards reducing energy waste and promoting sustainable energy practices.

**Thermal efficiency**

You are exactly right! The efficiency of a heat engine, which is a machine that transforms heat energy into work, is measured using thermal efficiency. This efficiency can be calculated using the formula:

η = (1 - Qc/Qh) x 100%

Where Qc is the heat that leaves the engine and Qh is the heat that enters the engine.

As you mentioned, there is a limit to the efficiency of a heat engine, which is given by Carnot's theorem. This theorem states that the maximum efficiency of a heat engine is determined by the temperatures of the heat sources. This maximum efficiency can be calculated using the formula:

η_max = (1 - Tc/Th) x 100%

Where Th is the temperature of the hotter source and Tc is the temperature of the colder source.

This means that no matter how much we try to minimize energy losses due to friction or other factors, the efficiency of a heat engine cannot exceed this maximum value. Therefore, maximizing the temperature difference between the heat sources is crucial to achieving higher efficiency in heat engines.

## 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: 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.

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 - 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.

## Efficiency in Physics

**What is efficiency in physics? **

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

**What is an example of efficiency in physics? **

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.

**What is the formula for calculating efficiency in physics? **

Generally, the formula for calculating the efficiency is:efficiency = (useful output energy transfer) / (total input energy transfer)

**What is the use of efficiency?**

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.

**What is the symbol for efficiency in physics?**

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