Law of Conservation of Energy
Last Updated : 30 Apr, 2024
Law of Conservation of Energy is the most fundamental law of physics which states that "Energy can neither be created nor be destroyed it can only change from one form of the energy to another form of the energy." It is the fundamental law of Physics that governs various processes in our environment.
Before learning deeply about the Law of Conservation of Energy we must know about Energy. Energy is the capacity of the object to do work, It is a physical quantity that allows an object to do different types of work.
Let's learn more about the Law of Conservation of Energy, and others in detail in this article.
What is Energy?
Energy is that ability that helps in applying force in order to do some work. It is simply that force that causes things to move. The capacity to do work is known as Energy. One very important fact about energy to note is that even though, energy occurs in many forms and has so many types, from kinetic energy to potential energy to solar energy, etc. The SI Unit of energy is Joules. Apart from joules, other units of Energy are ⇢ Calories, Horsepower, Kilowatt (kW)-Power, and Kilowatt-hour (kWh). There are many different forms of energy, following list shows and describes some of the important aspects of mechanical energy:
- Kinetic Energy: Kinetic Energy is the energy that is possessed by the objects in motion. Work must be done on an object to change its kinetic energy. It is usually expressed in the form of the equation 1/2mv2.
- Potential Energy: Potential energy is defined as the energy that is possessed by an object by virtue of its position. The potential energy is denoted by "mgh" where "h" is the height of the object.
- Mechanical Energy: This energy is the total energy associated with the position and velocity that is stored in the object. Hence, mechanical energy is the sum of kinetic energy and potential energy.
- Chemical Energy: Chemical energy is defined as the energy that is stored inside the bonds in the materials. This energy is involved in the formation or destruction of chemical bonds.
- Nuclear Energy: This energy is defined as the energy that is produced or consumed in the processes where nuclei of atoms are involved.
Energy Conservation
From the above examples, it is clear that the total energy of the system is always conserved it can only be converted from one form to another. It wastes lots of our energy by converting one form of energy into another form. So we must use our energy resources widely this is called energy conservation.
What is the Law of Conservation of Energy?
It's known that the total mechanical energy of the system remains constant if the forces working on the system are conservative in nature. Potential energy and kinetic energies keep interchanging with each other. In the case of non-conservative forces, these energies are converted to some other energy such as heat, noise, etc. In the case of a system that is isolated from the outside world, the total energy remains constant.
In an isolated system, energy can neither be created nor be destroyed. Total energy remains constant. It can be converted from one form to another form.
The principles of conservation of energy cannot be proved however no violation of this law has ever been observed. So, it is widely accepted with proof.
For an isolated system, the loss of energy in some part is followed by a gain of an equal amount of energy in some other part of the system. This principle is not yet proven but no exception of this principle is yet encountered by physicists so it is considered to be true.
The law of conservation of energy can easily be understood by the following example, here in the image given below the total energy of the cyclist at the bottom of the hill is in the form of Kinetic Energy only, and at the top of the hill is in form of potential energy.
The total amount of energy in any system is calculated using the following equation:
UT = Ui + W + Q
Where,
- UT is total energy of a system,
- Ui is initial energy of a system,
- Q is heat added or removed from the system, and
- W is work done by or on the system.
Also, change in the internal energy of the system is calculated using,
ΔU = W + Q
Law of Conservation of Energy Derivation
Law of Conservation of Energy can be derived with the help of the following example, take a ball falling from the height H and the initial velocity is zero, also the potential energy at the surface of the earth is zero.
Now at the height H from the ground,
Etotal = Epotential + Ekinetic
⇒ Etotal = 1/2mv2 + mgH
⇒ Etotal = 1/2m(0)2 + mgH
⇒ Etotal = mgH...(A)
As the ball falls to the ground, its potential energy decreases, and kinetic energy increases.
At any point B, which is at a height X from the ground, it has speed 'v' as it reaches point B. So, at this point, it has both kinetic and potential energy.
Etotal = Epotential + Ekinetic...(1)
and Epotential = mgX...(2)
According to the third equation of motion,
v2 = 2g(H-X)
⇒ 1/2mv2 = 1/2m×2g(H-X)
⇒ 1/2mv2 = 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,
v2 = 2g(H-0)
⇒ 1/2mv2 = 1/2m×2g(H)
⇒ 1/2mv2 = mg(H)
⇒ Ekinetic = mg(H)...(c)
Using (a), (b), and (c)
E = mg(H) + 0
⇒ E = mgH...(C)
Thus, from A, B, and C it is clear that the total energy at any point of the falling of the ball is constant (mgH).
Law of Conservation of Energy Examples
Various events or examples we see in our daily life support the Law of Conservation of Energy. Some of the examples to prove the law of Conservation of Energy are discussed below in this article.
- Engines convert chemical energy into mechanical energy.
- An electric motor converts electrical energy into mechanical energy.
- Electric bulb converts electric energy into light and heat energy.
- Hydroelectric power plants convert the potential energy of water into the kinetic energy of the turbine, which is further converted into electrical energy.
- Loudspeaker converts electrical energy into sound energy and some portion of the energy is dissipated in the form of heat.
- An electrochemical cell converts chemical energy into electric energy and vice versa.
Application of Conservation of Energy
There are various applications for the conservation of Energy as it is widely used in various processes which we observed in our daily life. Some of the processes in which conservation of energy is applied are,
- A car engine converts the chemical energy of the fuel into mechanical energy and enables the car to run.
- The energy we get from the food we eat is an example of conservation of energy as the chemical energy of the food is changed into various forms of energy by our body to do various life processes.
- A hydroelectric power dam uses the potential energy of the water to rotate its turbine which in turn produces electrical energy.
- A moving car hits another car at rest transfers its energy to the other car and the other car gains some motion.
- A player hitting a ball from his bat uses his mechanical energy to give kinetic energy to the ball.
- An electric generator uses the chemical energy of the fuel to run its engine which in turn rotates a coil that produces electric energy.
In all the above examples the conservation of energy holds true as the energy in all the cases is neither created nor gets destroyed it only changes its form.
Why Can Perpetual Motion Machines Never Work?
We can create a machine that when given some energy must run for infinity only changing its form of energy. These types of machines are called perpetual machines and theoretically, they can run forever but the second law of thermodynamics does not allow for the making of these machines as every time the energy changes its form some of the energy gets wasted.
For, example if we create a Perpetual Motion Machines that take the potential energy of the water stored at some height and allow it to change that energy into mechanical energy which in turn uses this mechanical energy to store water again at that height, and this loop is continued till infinity. This is true in theoretical case but in reality, this machine loses some energy in the form of friction, air drag, and other, and in every cycle, a significant amount of energy gets wasted which in turn cause the machine to stop after some time.
Thus perpetual motion machines never work for infinite cycles and they only work for a finite cycle.
Also, Check
Solved Examples on Conservation of Energy
Example 1: Find the work done when a force of F = x + 3 produces a displacement of 3 m.
Solution:
Work done by a variable force is given by,
W = ∫Fdx
F(x) = x + 3
Calculating the work done.
W = \int^{x}_{0}Fdx \\ = \int^{x}_{0}(x + 3)dx \\ = [\frac{x^2}{2} + 3x]^{x}_{0} \\ = \frac{x^2}{2} + 3x
Here, the displacement is x = 3
W = x2/3 + 4x (at x = 3)
⇒ W = 32/3 + 4(3)
⇒ W = 15 J
Example 2: The work being done on a system is given by the following equation, W = 3t2
Calculate the instantaneous power at t = 4.
Solution:
Instantaneous power is given by,
P = dW/dt
Given: W = 3t2
Calculating power, P = dW/dt
P = \frac{d(3t^2)}{dt}
⇒ P = 6t
At, t = 4
P = 6(4)
⇒ P = 24 J
Example 3: The work being done on a system is given by the following equation, W = t3 + 5t + 10
Calculate the instantaneous power at t = 2.
Solution:
Instantaneous power is given by,
P = dW/dt
Given:
W = t3 + 5t + 10
Calculating power,
P = dW/dt
⇒ P = \frac{d(t^3 + 5t + 10)}{dt}
⇒ P = 3t2 + 5
At, t = 2
P = 3(t2) + 5
⇒ P = 3(22) + 5 J
⇒ P = 3(4) + 5
⇒ P = 17 J
Example 4: An object is kept at a height of 20m. It starts falling towards the ground. Find the velocity of the object just before it touches the ground.
Solution:
Potential energy at the start will be equal to the kinetic energy just before touching the ground.
P. E = K. E
mgh = 1/2mv2
Given:
g = 10
h = 20 m
Plugging the values inside the equation,
mgh = 1/2mv2
⇒ 2gh = v2
⇒ v = \sqrt{2gh}
⇒ v = \sqrt{2 \times 10 \times 20}
⇒ v = 20 m/s.
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What is Frequency?Frequency is the rate at which the repetitive event that occurs over a specific period. Frequency shows the oscillations of waves, operation of electrical circuits and the recognition of sound. The frequency is the basic concept for different fields from physics and engineering to music and many mor
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Amplitude, Time Period and Frequency of a VibrationSound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in a vacuum because there is no material to transfer sound waves. Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is
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Energy of a Wave FormulaWave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds signifi
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Simple Harmonic MotionSimple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the memb
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Displacement in Simple Harmonic MotionThe Oscillatory Motion has a big part to play in the world of Physics. Oscillatory motions are said to be harmonic if the displacement of the oscillatory body can be expressed as a function of sine or cosine of an angle depending upon time. In Harmonic Oscillations, the limits of oscillations on eit
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Sound
Production and Propagation of SoundHave you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
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What are the Characteristics of Sound Waves?Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
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Speed of SoundSpeed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
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Reflection of SoundReflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
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Refraction of SoundA sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
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How do we hear?Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
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Audible and Inaudible SoundsWe hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
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Explain the Working and Application of SONARSound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
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Noise PollutionNoise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
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Doppler Effect - Definition, Formula, ExamplesDoppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
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Doppler Shift FormulaWhen it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
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Electrostatics
ElectrostaticsElectrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force.Electrostatic forces are non cont
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Electric ChargeElectric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
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Coulomb's LawCoulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
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Electric DipoleAn electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
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Dipole MomentTwo small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
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Electrostatic PotentialElectrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
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Electric Potential EnergyElectrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field.Sometimes electrical potential energy is confused with electric pot
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Potential due to an Electric DipoleThe potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
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Equipotential SurfacesWhen an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
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Capacitor and CapacitanceCapacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
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