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# Conservation of Energy Formula

Energy is required for the evolution and existence of life in any form on the Earth. In Physics, it is defined as the capacity to do work. We all know that energy exists in different forms in nature. You have learned about various forms of energy like heat, electrical, chemical, and nuclear, etc. In this article, the student will learn about the law of conservation of energy and conservation of energy formula.

Source:en.wikipedia.org

## Conservation of energy formula

### What is the Law of Conservation of Energy?

In the simplest words, we can say that energy is the ability or capacity to do some work. Thus energy is required to perform some activity or work in our day to day life. We need the energy to walk, run, drive, cook, jump, play, pull objects and for many more tasks. Energy is also essential for any vehicle to move and machines to run and bulbs to glow.

The law of conservation of energy is a very important law in thermodynamics study in Physics. According to it energy can neither be created nor be destroyed. But we may transform it from one form to another. If we take all forms of energy into consideration, then the total energy of an isolated system always remains constant. All kinds of energy follow the law of conservation of energy.

Source: en.wikipedia.org

### The formula for Conservation of Energy

Some of the most common forms of energy are heat energy, light energy, electrical energy, chemical energy, tidal energy, gravitational energy, etc. One form of energy can be transferred to another form due to some actions. But the sum total of the energy value will always be the same. This is the law of conservation of energy.

The statement of conservation of energy can be written as,

Energy spent in one activity = Energy gained in the other activity.

For a given system, we can write,

$$\Delta E_{sys} = E_{in} – E_{out}$$

The net amount of energy transfer into or out of any system occurs in various forms Such as heat (Q), mass (m) and work (W). Hence, we can rewrite the aforementioned equation as:

$$E_{in}−E_{out} = Q−W$$

By dividing all the terms into both sides of the above equation by the mass of the system, this equation will represent the law of conservation of energy on a unit mass basis. This is being shown below:

$$Q−W= \Delta E$$

Therefore, we can write the conservation of energy rate equation as:

$$Q−W=\frac {d}{dt} E$$

Where,

 $$E-{sys}$$ The energy of the system as a whole $$E_{in}$$ Incoming energy $$E_{out}$$ Outgoing energy E Energy Q Heat m Mass W Work t Time

### Some Real-Life Examples

We have the example of a windmill. The mechanical energy of the wind rotates the turbines of the windmill. It, in turn, rotates the shaft of an electric generator, and hence generating the electrical energy. Here, we can see that the mechanical energy of wind gets converted into electrical energy.

### Solved Examples

Q. 1: The initial energy and the final energy of a system are 2950 J and 5860 J respectively. Compute the energy conservation of the system.

Solution:

We can use the following formula to compute the energy conservation of the system:

$$\Delta E_{sys} = E_{in} – E_{out}$$

= 5860 – 2950

= 2910 J

Therefore, Energy conservation of the system is 2910 J.

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