The Law Of Conservation Of Energy: Principles, & Examples

In this world, we all follow certain rules. The things that work around us, the way we function – everything adheres to particular laws. Now, one of these important laws is the law of conservation of energy. The name is pretty self-explanatory. But let's get into more detail about this law. Read on, and you'll understand how important it is in daily life.

What is the Law of Conservation of Energy?

The idea to be explored is very simple. Suppose your teacher provides you with a certain amount of clay. Now, you must make shapes out of it. First, you make an elephant. Then, you create a car. The two things are completely different. But you use the same amount of clay to make both. The form changes, but the amount remains constant.

That’s pretty easy to understand, right? Well, the principle of the conservation of energy works the same. The total amount of it present in an isolated system remains constant. According to this law, you cannot create or destroy it. You can only convert one form to another. Let’s take a familiar example. You must be familiar with light bulbs. How do they work?

The electric energy in the bulb transforms into light. That's why, when you turn on a bulb, light emanates from it. But wait, there is more to it! Touch the surface of the light bulb when it’s on. You’ll notice that the surface is slightly warm. That’s because the electric energy isn’t completely converted to light. Some of it transforms to heat. Neither heat nor light is created out of nothing. They are merely transformed.

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What is Energy?

What do you say when you’re too tired to do any work? “I’m out of energy!” Well, physics considers it to be the strength to do any work. It is a quantitative property that transfers from one object to another. In other words, you can calculate it. The standard unit for that is Joule. However, you can also express it in other units of measurement, such as the following –

• Kilowatt
• British Thermal Units
• Calories
• Kilocalories
• Ergs
• Horsepower

Energy is an umbrella term. If you dig into it, there are so many different kinds of energies that fall under it. Let’s explore them in the next section. Scroll down.

What are the Different Types of Energy?

When you think about energy, two kinds usually pop up in your mind immediately – kinetic and potential. Let’s explore them in greater detail.

1. Kinetic energy

This is contained in moving objects. Whenever an object moves, it can cause certain changes. It can also produce work. For example, when a car is in motion, it can help people move from one place to the other. In other words, it causes displacement. But when the car is static, no change or work occurs.

Now, kinetic can be of different kinds. Let’s check them out.

Electrical

In a circuit, charged electrons move from one point to the other. The energy produced in this case is electrical.

Thermal

The energy produced in a system due to the rise or fall of temperature is called thermal. It is directly proportional to the temperature fluctuation. Let’s simplify this further. When temperatures rise, the movement of molecules and atoms increases. This causes them to collide more. Thus, you generate more thermal energy. The reverse is also true. When temperatures fall, it drops.

Mechanical

The position and motion of an object determine its mechanical energy. Does that make things confusing? Well, let's put it this way. Add potential energy and kinetic energy. The result is your answer.

Radiant

The name is self-explanatory. But let’s understand what this entails. Radiant energy radiates. You’ll find this mostly for electromagnetic and gravitational radiation. Let’s take an example. First, light a candle. What do you observe? You get light and heat. Both emanate from the candle because they are waves. This is called radiant.

Sound

How do you think you hear your professors during a lecture? In this case, your professor is the source of the sound. When they speak, the sound waves go outward and reach your ears. These waves reach your eardrums and vibrate. The vibrational energy converts to electrical and reaches your brain.

2. Potential energy

When a body or object remains in static motion, it contains potential energy. This energy depends on a few factors –

• The physical properties of the object
• The object’s position in relation to other objects

Like kinetic, you’ll find many types of potential energy.

Chemical

Chemical bonds are present in all objects. The energy stored in these bonds is called chemical. Whenever there is a change in the particle number, this chemical energy is released or absorbed.

Electric

The energy you need to move a charge against an electric field is called electric potential. Let’s look at an example. Potential electric energy is stored in a television that is turned off.

Elastic

When you deform an elastic object, elastic potential energy is stored within that object. Remove that external force, and it is released. Let’s take the example of an archer. When the archer nocks the arrow on the bow, they pull the bowstring taut. Thus, an external force is applied. The string now contains elastic potential energy.

Gravitational

When an object is present in a gravitational field, it contains gravitational potential energy. Every object or person on earth contains it. That’s because of the earth’s gravitational pull. Now, imagine what will happen if this pull goes away. We would all fly off into space.

Nuclear

The potential energy that is present in the protons and neutrons in the nuclei of an atom is called nuclear potential. The protons are positively charged. Like charges repel each other. That's why the neutrons in the atom have to exert force on the protons to keep them from breaking the structure.

Now you have a clear idea of the different types of energies. It’ll be easier for you to understand conversions. One kind can convert to the other through various reactions. That’s how the conservation of energy happens.

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

Till now, you've been told that you cannot create or destroy energy. The law clearly states that it remains constant. But if that is not the case? Well, let's seriously consider this hypothetical situation in more detail.

The basic concept of the law of conservation is that there is no energy loss. In a closed system, it merely changes its form. For example, the electrical energy needed to light a bulb gets converted to light and heat. Now, some form of it is lost due to various factors. But the overall amount in the system remains constant.

But what happens if the lost energy leaves the system? Everything will come to an abrupt halt once the total amount in the system is depleted. Machines will stop working. Human beings will stop functioning. Such a situation has never been noticed. That’s why, even though the principle of conservation of energy cannot be proved, everyone believes it to be true.

What is the Conservation of Energy Formula?

The conservation of energy formula emphasizes the constant nature. You cannot create it. Neither can you destroy it. Even if there is some loss during the conversion, it remains within the system. So, the total amount in the system remains constant. You can express this via a formula as well. Let’s check it out.

U_T = U_i + W + Q

In this formula,

U_T = The total energy present in a system

U_i= The initial energy present in a system

W = Any work done by the system or done on the system

Q = The heat added to the system or removed from the system

As you can see, the formula takes into account any energy loss or addition in the overall system. The total remains constant despite them. There’s a formula to denote a change in the internal energy as well. Check it out for future reference –

ΔU = W + Q

These formulas can be challenging to decipher. But don’t worry! The main formula agrees that the total energy in the system remains constant. So, you need not stress about the hypothetical situation where energy is not conserved.

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Derivation of the Law of Conservation of Energy Equation

Let’s derive the law of conservation. This will be a simple process. For this, you have to consider a hypothetical situation.

Consider an object falling to the ground from a height. The potential energy on the earth's surface is zero. Now, for something to fall, it has to be at a particular height, right? Consider that height to be 'H.' Therefore, the distance between the earth's surface and the position of the object is 'H.' Now, let the position where the object is be 'A.' At this position, the object is static. So, its velocity here is zero. Naturally, the object has the highest potential energy at 'A.'

Thus, you can write –

E = mgH …… (1) [Here, E = potential energy, m = mass of the object, g = the gravitational force, and H = the height of the object]

When the object falls from point 'A,' its potential starts decreasing. Consequently, its kinetic keeps increasing. The object will keep falling because of the gravitational pull. While falling, let it reach point 'B.' This position is at a height of 'X'  from above the ground. At this position, the object contains potential and kinetic energy.

Now, the total energy present in the object is kinetic and potential. Therefore, you can express it as the following –

E = K.E + P.E [where E = total energy, K.E = kinetic energy, and P.E = potential energy]

You can also express this as –

P.E = mgX …… (2) [where P.E = potential energy, m = mass of the object, g = gravitational force, X = distance of the object from the ground]

For the next step, you must understand the Third Equation of Motion. It is also known by two variations –

• Velocity-position relation
• Velocity-displacement relation

According to this equation, the final velocity of an object is denoted as –

v² = u² + 2as

Here, the terms stand for –

v = final velocity of the object

u = initial velocity of the object

a = the constant acceleration at which the object moves (no external force to increase acceleration)

s = the displacement that happens to the object because of its motion within time ‘t’

Now, let’s go back to where you paused. You know the formula for the final velocity of an object. You can therefore write –

v² = 2g(H-X)

Why? Let’s explain it a bit. The initial velocity of the object was zero since it was static. Therefore, u² remains zero. Now, the displacement is the distance it has covered. Initially, it was at height 'H.' Currently, it is at height 'X.' Therefore, the distance it has covered is the difference between the initial and the final position. Now, let's see how the equation progresses.

v² = 2g(H-X)

or, m X v^{2 =} m X 2g(H-X) [multiplying both sides by m]

or, K.E = m X 2g(H-X) [since K.E = mv²]

or, K.E = mg(H-X) …… (3)

Now, let’s consider the three equations (1), (2), and (3) at once. This will give you the following –

E = K.E + P.E

or, E = mg(H-X) + mgX

or, E = mgH – mgX + mgX

or, E = mgH

So, at height 'X,' the energy is mgH.

While falling, the potential energy of the object decreases while the kinetic increases. When it reaches the ground, suppose it is at point C. Here, the object becomes stationary again. Therefore, you can write –

E = P.E + K.E

Now, P.E = 0 (since the height is zero)

Therefore, E = K.E …… (4)

Let’s go back to the Third Equation of Motion again. You can write –

v² = 2g(H-0)

or, m X v²= m X 2gH

or, m X v²= mgH

or, K.E = mgH

Now, we know E = K.E + P.E

or, E = mgH + 0

or, E = mgH

Thus, you have already established that the energy at any point during the falling of the object remains constant. This proves the law of conservation.

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What are Some Law of Conservation of Energy Examples?

You’ll find numerous examples of the law of conservation around you. Look carefully all around. Can’t detect any? Let’s make things simpler for you. Take a look at the list below. You might be surprised by a few.

• Chemical to mechanical – Machines
• Electrical to sound – Loudspeakers
• Electrical to mechanical  – Electric motor
• Chemical to electric – Electrochemical cell
• Electric to light and heat – Light bulb
• Potential to kinetic to electrical – Hydroelectric power plants
• Wind to mechanical or electric – Windmills
• Heat to mechanical – Steam engines
• Electric to heat – Electric heater

See how so many machines around you use the law of conservation to function? Well, in this section, you’ve merely covered the types of conversion. Now, let’s check some real-life applications.

Real-life Examples of the Law of Conservation of Energy

Many things around you happen because of the law of conservation. This law is pretty simple. It states that energy can only be converted. You cannot create or destroy it. It must be constant. Now, read on to check how real-life situations can be explained using this concept.

1. The way human bodies function

You feel low on energy when you’re hungry. There’s no motivation to work. But what happens when you have your meal? You get the required energy to continue your work. How does that happen? Simple! Food contains chemical energy. When you consume food, this is converted to various other forms. This gives you the power to perform bodily functions.

2. When a car crashes into another vehicle

When a car is standing still, it has potential energy. Now, another car moving towards it has kinetic energy. When this moving car crashes into the static one, some of the kinetic energy is transferred to the still car. This results in the car moving a bit.

3. The workings of a coal-fired power plant

Multiple conversions take place in a coal-fired power plant. Let’s break them down. Coal contains chemical energy. When combustion occurs, this is converted to thermal. Thus, heat is generated. It is present in the exhaust gases. A heat exchanger transfers the thermal energy to steam.

4. Workings of an electric generator

What do you do when the electricity goes out? An electric generator comes in handy. This machine works in a very simple manner. It uses fuel to function. When you turn it on, the engine rotates a coil. This leads to the chemical energy to be converted to electric.

Notice how such simple tasks follow the law of conservation? No loss happens in any of the examples given. You can’t create as well. All you can do is convert it. It’s pretty simple, isn’t it? Did you ever think so many steps and conversions happen for things to work? Look around and try to find more examples from your surroundings.

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What Prevents Perpetual Motion Machines from Working?

Theoretically, perpetual motion machines are supposed to work forever. Here’s how it works. Once you supply some energy to the machine, it works in a cyclical manner by changing its form. Let’s take an example.

Suppose water is stored at some height. It contains potential energy. Now, you want to convert it into mechanical. Using this, you want to store the water at the same height. Thus, you get back to potential energy. This loop continues, creating a machine that never stops working. Theory says this can work.

But practically, it is impossible. That is only because of the second law of thermodynamics. According to this law, transformation usually results in the loss of energy. So, let’s go back to the earlier example. When using the perpetual motion machine, energy loss happens. This takes place because of air drag, friction, and other issues. With every cycle, more energy is lost. As a result, the machine will stop working after some time. That's why such a machine cannot exist.

Frequently Asked Questions

Q.1 What is the law of conservation of energyalso known as?

The law of conservation is also called the First Law of Thermodynamics. According to this law, you cannot create or destroy energy. It is only possible to change it from one form to the other. The total amount in the isolated system will remain constant.

Q.2. In which kind of system does the law of conservation apply?

The law of conservation is applicable to all kinds of closed systems. A closed system is isolated from everything else. This ensures that the energy within it cannot escape the system. It will always remain constant.

Q.3. What are the different types of energies?

The different kinds of energy are kinetic and potential. However, various types of energies fall under them. Under kinetic, you have electrical, thermal, mechanical, radiant, and sound. For potential, you have chemical, electric, elastic, gravitational, and nuclear.

Q.4. What are perpetual motion machines?

Perpetual motion machines are devices that work forever when you provide them with some energy. Theoretically, it's viable. The machine converts energies in a cyclical manner. Ideally, it should never stop. But practically, it's impossible. During conversion, some energy is dissipated because of external factors. Thus, the machine will stop working eventually.

Q.5. Who came up with the law of conservation of energy?

You can give the credit to Julius Robert von Mayer. But he’s not the only person who deserves the recognition. Other notable figures worth mentioning are James Prescott Joule and Hermann von Helmholtz. These incredible minds had a great contribution to the law of conservation of energy.

Q.6. What kind of conversion do you observe when a block slides down a slope?

When a block is on top of the slope, it is still. Since there’s no movement, it has potential energy. Now, give some external force to it. The block will slide down the slope. It’s in motion. Therefore, the potential energy slowly changes to kinetic.

Q.7. State an example where kinetic energy is converted to potential.

Consider a water tank at the top of a building. You pump the water from the ground to the tank on the top. The water flows through the pipes until it reaches the tank. While the water flows, it possesses kinetic energy. However, as soon as it reaches the tank, that kinetic energy transforms into potential.

Q.8. What does the term ‘energy’ mean?

'Energy' is the capacity to do any work. It is quantifiable and can exist in various forms. Some of them are mechanical, elastic, gravitational, and nuclear. One of its important characteristics is its inability to be created or destroyed. But you can change its form.

Q.9. State some examples of the law of conservation of energy.

Some examples of the law of conservation of energy are –

• Chemical to mechanical– Machines
• Electrical to sound– Loudspeakers
• Electrical to mechanical– Electric motor
• Chemical to electric– Electrochemical cell
• Electric to light and heat– Light bulb
• Potential to kinetic to electrical– Hydroelectric power plants

Q.10. What would happen if energy is not conserved?

If energy is not conserved, all living beings and machines will stop working after a certain point. Human beings, living organisms, and machines function because the energy present in the system is constant. It changes form but doesn't leave the system. If it does, then once all the energy leaves, everything will stop working.