The Principle of Conservation of Energy: Definition, Formula and Examples

The law of conservation of energy states that for an isolated system the total energy always remains conserved. This law is first proposed by Emilie du Chatelet which means energy can neither be created nor be destroyed, it can only be transformed from one form to another form.

•  Conservation of energy according to classic physics is distinct from conservation of mass. However, according to special relativity, mass is related to energy and vice versa by equation E = mc².
• The development of living forms on Earth necessitates the use of energy. It is defined as the ability to perform work in physics. We know that energy occurs in nature in various forms. the various forms of energy are heat energy, electricity, chemical energy, nuclear energy, and so on.

Key Terms: Energy, Law of Conservation energy, mass, heat energy, nuclear energy, Transformation of Energy

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What is the Energy Conservation Law?

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Energy cannot be generated or destroyed, according to the rule of conservation of energy.

• It may, however, be changed from one form to another. When all kinds of energy are considered, the total energy of an isolated system is always Constant.
• If there is a loss of energy in one area of an isolated system like the cosmos, there must be a gain of energy in another section of the universe.
• There is no known case of the concept of energy conservation being violated, despite the fact that it cannot be proved.
• The law of conservation of energy applies to all types of energy. In a nutshell, the law of energy conservation asserts that-:

“The total energy of a closed system, that is, one that is separated from its surroundings, is preserved.”

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The following equation determines the quantity of energy in any system:

\(U_T = U_i + W + Q\)

Where

• The total energy of a system is U_T.
• The initial energy of a system is called U_i.
• The heat generated or withdrawn from the system is denoted by Q.
• W denotes the amount of work done by or on the system.

The equation is used to calculate the change in the system's internal energy.

\(\Delta U = W + Q\)

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Energy Derivation- Law of Conservation

Assuming that the potential energy at the earth's surface is zero. Consider the case of a fruit falling from a tree.

Consider point A on the tree at a height of ‘H' from the ground; the fruit's velocity is zero, therefore potential energy is highest there.

E = mgH   ...(1)

The fruit's potential energy decreases as it falls, but its kinetic energy increases.

The fruit is falling freely under gravity towards the bottom of the tree at point B, and it is at a height X from the ground, and it has speed as it reaches point B. As a result, it will have both kinetic and potential energy at this moment.

E = K.E + P.E 

P.E =  mgX    ...(2) 

According to the third equation of motion, 

v₂ = 2g(H–X)

⇒12mv₂ =12m.2g(H–X)

⇒K.E=12m.2g(H–X)

⇒K.E=mg(H–X) 

K.E=mg(H-X)   ...(3) 

Using (1), (2), and (3) 

E = mg(H – X) + mgX 

E = mg(H – X + X) 

E = mgH

Similarly, if we look at the energy at point C, which is at the bottom of the tree, we get mgH. As the fruit falls to the bottom, we can observe how potential energy is being transformed into kinetic energy. As a result, there must be a point at which kinetic energy equals potential energy. Assume we need to determine the height ‘x' above the ground. At that time, we know,

K.E = P.E 

=> P.E = K.E = E₂    ...(4) 

E₂ is new energy obtained 

Where, E = mgH₂ 

H₂ is the new height. 

As the body is, from the ground, at height X, 

P.E = mgX    ...(5) 

Using (4) and (5) we get, 

mgX = mgH₂

⇒ X = H₂

The new height is referred to as H₂.

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Conservation of Energy

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Energy conservation is not the same as restricting the use of finite resources that will eventually run out.

• Reduced demand on a restricted supply would be the optimum method to save, allowing the supply to begin to rebuild itself.
• Often, the easiest method to accomplish this is to switch to a different energy source.

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Examples of the Law of Conservation of Energy

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Most inventions in physics are based on the notion that energy is conserved when it is moved from one form to another. Several electrical and mechanical devices work purely on the principle of energy conservation. We'll go through a few instances in this section.

Read More: Valance Electrons

• The chemical energy of the batteries is turned into electrical energy in a torch, which is then converted into light and heat.
• Waterfalls from a height on the turbines at hydroelectric power facilities. This causes the turbines to spin and create energy. As a result, water's potential energy is transformed into the turbine's kinetic energy, which is then translated into electrical energy.
• Electrical energy is transformed into sound energy in a loudspeaker.
• Sound energy is transformed into electrical energy in a microphone.
• Mechanical energy is transformed into electrical energy in a generator.
• Chemical energy is transformed into heat and light energy when fuels are burned.
• When food is broken down in the body, chemical energy is transformed into thermal energy, which is needed to keep the body warm.

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Things to Remember

• The development of living forms on Earth necessitates the use of energy.
• Energy cannot be generated or destroyed, according to the rule of conservation of energy. It may, however, be changed from one form to another. When all kinds of energy are considered, the total energy of an isolated system is always Constant.
• The law of conservation of energy applies to all types of energy.
• The total energy of a system is U_T.
• The initial energy of a system is called U_i.
• The heat generated or withdrawn from the system is denoted by Q.
• Energy conservation is not the same as restricting the use of finite resources that will eventually run out.
• The chemical energy of the batteries is turned into electrical energy in a torch, which is then converted into light and heat.