What is the Principle of Conservation of Energy?: Explained!

There are some concepts that keep students confused. For physics students, some work, power, and energy topics become incomprehensible. One such concept from 'Work, Power and Energy' is "What is the Principle of Conservation of Energy?"

Whether it is about its definition or derivation, everything just doesn’t stick to students’ minds and leads to poor academic performance. Therefore, it is vital to get clarity on each and every part of such a topic. If something is missed, scholars cannot reflect it efficiently in their assignments and get poor results.

This makes students seek assignment help online. Nowadays, there are numerous online platforms available that offer extraordinary academic writing services for university students. Such service providers create outstanding assignments for students and help them excel in their university studies.

However, even if you take aid from professionals, it is vital to get clarity on the topic you are submitting the assignment on. To help you out, everything related to this concept, including definition, principle, derivation, consequences, and examples, are assimilated together.

Read this write-up and clear all your doubts about the Conservation of Energy!

Definition of the Principle of Conservation of Energy

The principle of conservation of energy states that energy can neither be created nor destroyed. However, it can be changed to forms. If every form of energy is taken into account, then the overall energy of an isolated system is invariably constant. Furthermore, all the different forms in which energy exists follow this principle.

Therefore, in the case of an isolated set-up such as the universe, if some part of the energy gets lost, then an equivalent amount of energy will be added to any part of the universe. Even if this principle does not have any proof, at the same time, there is not any example that goes against this law. 

Conservative energy forms, such as kinetic energy and potential energy, keep interchanging with one another. Whereas, in the case of non-conservative energy, the conversion takes place either in the form of noise or heat.

The law of conservation of energy can be further understood in a much clearer manner with the following example:

Suppose a block skids from an inclined surface. When this action occurs, potential energy gets transformed into kinetic energy.  Due to friction, when the block slows down and stops moving, the kinetic energy is now thermal energy.

Therefore, it showcases how energy is indestructible. It just changes itself into different forms, right from potential energy to kinetic energy and ultimately to thermal energy.

Hence, the overall energy remaining in a system is calculated using the following formula:

UT = Ui + W + Q

In this equation,

• UT is the overall energy of a system,
• Ui is the initial energy of a system,
• Q is heat added or removed from the system, and
• W is the total work done by or on the system.

Moreover, the transition in the internal energy of the set-up can be calculated with,

ΔU = W + Q

Derivation of the Law of Conservation of Energy

Let us consider the potential energy on the surface of the earth to be 0. If a fruit falls from the tree, the point from where it falls is considered as A. If point A is at ‘H’ height from the surface, then the speed of the fruit at this point is 0. This makes potential energy at this point to be the maximum.

E = mgH —> (1)

While falling down, the potential energy of the fruit will decrease, and at the same time, its kinetic energy increase. At point ‘B’ (A point near the bottom of the surface), the height from the ground is ‘X.’ At this point, it will have both kinetic energy and potential energy in it.

E = K.E + P.E

P.E = mg X —> (2)

As per the motion’s third equation,

Etotal = Epotential + Ekinetic

⇒ Etotal = 1/2mv^2 + mgH

⇒ Etotal = 1/2m(0)^2 + mgH

⇒ Etotal = mgH…(A)

v^2 = 2g(H-X)

⇒ 1/2mv^2 = 1/2m×2g(H-X)

⇒ 1/2mv^2 = mg(H-X)

⇒ Ekinetic = mg(H-X)…(2)

Using (1), (2), and (3)

E = mg(H – X) + mgX

⇒ E = mg(H – X + X)

⇒ E = mgH…(B)

Also, at point C, at the ground,

Etotal = Epotential + Ekinetic…(a)

⇒ Epotential = 0…(b)  (as height is zero)

According to the third equation of motion,

v^2 = 2g(H-0)

⇒ 1/2mv^2 = 1/2m×2g(H)

⇒ 1/2mv^2 = mg(H)

⇒ Ekinetic = mg(H)…(c)

Using (a), (b), and (c)

E = mg(H) + 0

⇒ E = mg H…(C)

Thus, from A, B, and C, it is quite obvious that the total energy at any point when the fruit falls is constant, i.e., mg H

Examples of the Principle of Conservation of Energy

Maximum inventions of Physics are based on the statement that the energy is conserved while being transferred from one form to another. Numerous mechanical and electrical equipment keep working per the energy conservation law. It is clearer when you go through some of the examples given below:

• In a battery-operated lamp, the batteries' chemical energy is converted into electrical energy, which ultimately converts into light and heat energy.
• In hydroelectric power plants. When the water falls from a height on the turbine, this successively rotates the turbines and leads to the generation of electricity. Therefore, water’s potential is converted into the kinetic energy of the turbine. Later, the overall energy is transmitted into electrical energy.
• In a speaker, electrical energy transforms into mechanical energy.
• In the case of a microphone, electrical energy is formed out of mechanical energy.
• In a generator, mechanical energy gets interchanged with electrical energy.
• Chemical energy then changes into heat and light energy on burning of fuels.
• Food’s chemical energy gets converted to thermal energy when it breaks down after eating.
• In engines, chemical energy transforms into mechanical energy
• When it comes to electric motors, electrical energy changes to mechanical energy.
• Electric energy interchanges with light and heat energy in an electric bulb.
• Hydroelectricity-based power plants transform water's potential energy into the turbine's kinetic energy. Subsequently, it gets transformed into electrical energy.

The Consequence of the Principle of Conservation of Energy

Lenz’s Law is considered a result of the energy conservation principle.

As per Lenz’s law, when there is a closed circuit, the direction of the current induced in it is such that it is opposed to the variation in magnetic flux. This magnetic flux is the reason due to which the current is generated.  

To prove that Lenz’s law results from the law of energy conservation, let’s assume a bar magnet is being pushed toward a conducting loop.

When the N-pole moves in the direction of the loop, the side of the loop towards the north pole, it eventually gets north polarity. On the contrary, when the N-pole moves in the opposite direction of the face, it starts gaining south polarity. 

This means that the movement of the magnet changes its direction every time. Therefore, when any kind of work is done on the magnet, i.e., when the magnet moves toward or away from the loop, the mechanical energy is transmitted into electrical energy.

Therefore, the law of conservation of energy is precisely followed in Lenz’s law, and it turns out to be a consequence of the energy conversation law.

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