Efficiency Formula

We know that energy can be transformed into one form to another, at the same time it is impossible to have 100% conversion. Most of the devices are not designed to have 100% efficiency, leading to incomplete conversion of energies. In real life, there are no ideal devices that can perform with 100% efficiency. Efficiency is a physical term that is used to measure how much work is done or how much energy has been transferred during the process. The efficiency of any device can be calculated using the efficiency formula.

Efficiency can be defined as the ratio of the work done by a device or in a process to the total energy expended or heat consumed. In this article, we will discuss the efficiency formula, what is efficiency in physics along a few solved numerical problems for better understanding.

How to Calculate Efficiency?

Efficiency, in general, refers to how much energy or work has to be done for getting a desired or a particular outcome of the given input with as much less wastage as possible. Thus, we can say efficiency is the just ability of a device or process to minimise wasting materials, efforts, energy and time in performing something or producing the desired result.

Similarly, we can define energy efficiency as the ratio of the output of the energy to the energy input and then express it in the form of a percentage. If any process or device is said to be perfect if and only if it is capable of having an efficiency of 100%.

Generally, everyone gets confused with the term efficiency and effectiveness. Whereas, both efficiency and effectiveness are completely different from each other. In other words, we can say efficiency is when things are being done right or achieving the goal or output with minimum efforts. But, effectiveness refers to doing the right thing. For example, a car or any vehicle is said to be an effective form of transportation, if and only if the vehicle covers the maximum distance in minimum time. Similarly, the way it uses fuel to transport determines its efficiency.

So now, how to calculate efficiency?

The efficiency of any device can be calculated using the efficiency formula. The efficiency formula physics is given by the following expression:

⇒\[\eta = \frac{\textrm{Work output}}{\textrm{Work input}}\times\]100%

And, energy efficiency formula is given by:

⇒\[\eta = \frac{\textrm{Energy output}}{\textrm{Energy input}}\times\]100%

Efficiency Formula Physics?

So far we have discussed how to calculate efficiency in a general way, now let us have a look at the efficiency formula physics. In physics, the concept of efficiency or efficiency physics plays an important role, particularly in thermodynamics. Efficiency term is most commonly used for determining the capacity of a system or any engine. In physics, Carnot engines are the only devices that are considered to be ideal and capable of delivering 100% efficiency. 

According to thermodynamics, the efficiency of any thermal system is given by the following efficiency equation:

⇒\[\eta = \frac{\Delta Q}{Q}\]

Where,

ΔQ = Heat supplied - Heat rejected

Similarly, let us have a look at some more engines and their efficiencies.

• Otto cycle - The otto cycles are the heat engines and this engine utilises petrol as fuel. It has an efficiency of almost 58%.

• Diesel cycle- The Diesel engine uses diesel as fuel and the efficiency of diesel engines are estimated at almost up to 62%.

• Brayton cycle - The Brayton engine and is also known as the jet engine and it uses jet fuel. Its efficiency is estimated at almost 70%.

Thus, we can use the efficiency formula in different ways according to the desired result. The same efficiency formula is written in different formats depending on the output and input values, for example, Carnot cycle efficiency is calculated using change in heat and the amount of heat supplied, at the same time efficiency of any other system is calculated in terms of net work done to the total work done.

Examples

1) A particular thermodynamic process has an energy efficiency of only 5.00%. To complete this large-scale thermodynamical process, 1,60,000 Joules of energy is input. Then, what is the energy output of this process?

Sol:

Given,

The efficiency of the thermodynamical process = η = 5 %

The energy input of the thermodynamical process = Ein = 1.6 × 105  joules

Now we are asked to determine what is the energy output of the given thermodynamic process. We know that the energy efficiency formula is given by:

⇒\[\eta = \frac{\textrm{Energy output}}{\textrm{Energy input}}\times\]100%

Rearranging the above expression for energy output, and substituting the required values, we get:

⇒ E_out = \[\frac{\eta\times  E_{in}}{100％}\]

⇒ E_out = \[\frac{5\times1.6\times 10^{^{5}}}{100％}\] = 8000 joules

⇒ E_out = 8 Kj

Therefore, the energy output of the given thermodynamic process is 8 kJ.

1) A heat engine expels around 800 J of heat energy as useful work. Determine the total energy supplied to the heat engine as input if its efficiency is 60 %.

Sol:

Given,

The efficiency of the heat engine = \[\eta = 60 ％\]

The energy output of the heat engine = Eout = 800 joules

Now we are asked to determine what is the energy output of the given heat engine. We know that the energy efficiency formula is given by:

⇒\[\eta = \frac{\textrm{Energy output}}{\textrm{Energy input}}\times\]100%

Rearranging the above expression for energy input, and substituting the required values, we get:

⇒ E_out = \[\frac{E_{out}}{\eta }\times 100％\]

⇒ E_out = \[\frac{800}{60}\] = 1333.3 joules

⇒ E_out = 1.3 Kj

Therefore, the energy output of the given thermodynamic process is 1.3 kJ.