Law of Conservation of Energy

According to the Law of Conservation of Energy, energy can neither be created nor destroyed. It can only convert from one form to another. Both living and non-living beings use energy for multiple activities. Animals consume food to get energy, while machines get it from fuels or electricity. The sun gives out heat and light. From where does the sun get the energy to shine? Let us learn about it in this article.

What is Energy?

We do work. To do work, we need energy. So, the conservation of energy is defined as the capacity to do any work.

Work is the change effected in an object due to force applied to it. If the force applied to an object makes it move by a distance or changes its shape, then work is said to be done.

\({\rm{work = force \times distance}}\)

This concept of work is applicable to living beings as well as machines. Since energy is the capacity to do work, energy and work have the same unit, that is Joule.

Relation Between Power and Energy

Energy used in unit time to do work is Power. Or in other words, power is the rate at which work is done or energy is converted. To use energy, it must be converted from one form to another.

\({\rm{Power = \;\;}}\frac{{{\rm{work}}}}{{{\rm{time}}}}{\rm{ = }}\frac{{{\rm{energy}}}}{{{\rm{time}}}}\)

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Unit of Energy

The SI unit of energy is Joule. It is equal to the work done in moving an object by \(1\,{\rm{metre}}\) by a force of \(1\;{\rm{Newton}}.\)

\(1\;{\rm{Joule}} = 1\;{\rm{Newton}}\; \times 1\;{\rm{metre}}\)

Other units of energy that are specific to certain systems are:

1. kilowatt-hour \(\left( {{\rm{kWh}}} \right)\) which is used for electrical energy. This comes from the above relation where energy is the product of power (kilowatt) and time (hour).
2. electron volt \(\left( {{\rm{eV}}} \right)\) is the unit used in relation to atomic or nuclear energy.
3. British Thermal Unit \(\left( {{\rm{BTU}}} \right)\) is the amount of heat required to raise the temperature of one pound of water by \({1^{\rm{o}}}\,{\rm{F}}.\)
4. Calorie is the amount of heat required to raise the temperature of water by \({1^{\rm{o}}}\,{\rm{C}}.\) It is also the unit used for energy given out by food items.

Forms of Energy

Energy in this universe is available in many forms. For example, mechanical energy, thermal energy, light energy, sound energy, chemical energy, etc. Energy in one form can be converted to another form by using suitable equipment.

Practice Exam Questions

Mechanical Energy

Mechanical energy is of two types. (a) Potential energy (b) Kinetic energy.

Sum of the potential and kinetic energy of a particle or system of particles is called the total mechanical energy of the particle or the system.

a. Potential Energy

Energy that is related to the position of the object is potential energy. The position or internal structure of an object determines its potential energy.

For example, an arrow does not possess any potential energy when the bowstring is in a relaxed situation. But it gains enormous potential energy when the string is stretched. This energy possessed by the arrow can cause severe damage. Potential energy gained by the arrow due to the stretched bow is called elastic potential energy.

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Few types of potential energy:

i. Gravitational potential energy: The potential energy gained by the object due to its relative position in the gravitational field (say above the earth’s surface) is called gravitational potential energy.

If an object of mass \(m\) is at a height of \(h\) from the Earth’s surface, we can say that the object has a potential energy of \(mgh\) with respect to the Earth’s surface.

\(PE = mgh\)

Where,

\(m\) is mass of the object

\(g\) is acceleration due to gravity

\(h\) is height of the object from the reference point

Gravitational potential energy concept is utilized in the case of hydroelectricity where the difference in water level in a dam is used to turn the turbines.

ii. Elastic Potential Energy: We might have seen or used spring, rubber band or an elastic strip in our day-to-day life. When a force is applied to these objects, it creates tension or strain on them temporarily. When we release this force, releases the stress or strain on them to come back to their original shape. This movement is due to elastic energy.

The elastic potential energy stored in a stretched or compressed spring of spring constant \(k\) is

\(PE = \frac{1}{2}k{x^2}\)

Where,

  \(k\) is the constant

  \(x\) is the length of compression or extension from its relaxed position

b. Kinetic Energy

The energy possessed by an object due to its motion is kinetic energy. For aly falling object, its gravitational potential energy is converted to kinetic energy.

The kinetic energy of a moving object can be written as,

\(KE = \;\frac{1}{2}\,{\rm{m}}{{\rm{v}}^2}\)

where \(m\) is mass of the moving object, \(v\) is its velocity.

Conservation of Mechanical Energy

When there is no energy lost to the surroundings, the mechanical energy of the system i.e. sum of kinetic energy and potential energy remains constant.

\(KE + PE = {\rm{constant}}\)

Examples of Mechanical Energy:

1. A rock on a slope of a hill has potential energy due to its position or height from the base of the hill. If it starts rolling down, this potential energy gets converted to kinetic energy and has the power to crush small items that come in its way.
2. Water flowing down a pipe and rotating the turbines.
3. Energy in wind that makes leaves move, rotates windmills are a few examples.

Nuclear Energy

It is a form of energy stored in the nucleus of an atom. The nucleus of atoms consists of positively charged protons \(\left( + \right)\) and neutral neutrons. Like charges repel each other, therefore, a tremendous amount of energy is required to keep this nucleus together.

Energy is released from nuclei in two processes known as:

1. Nuclear Fission
2. Nuclear Fusion

1. Nuclear Fission: When a heavy nucleus such as that of uranium is split, an enormous amount of heat is created. This is called nuclear fission, that is, breaking up the nucleus.
2. Nuclear Fusion: When two or more light nuclei are fused together, then also an enormous amount of heat is generated. Stars such as the sun create heat and light by fusion.

In both these processes, some mass of the nucleus is lost. This lost mass is converted to heat energy, as given by the famous energy equation by Albert Einstein

\(E = m{c^2}\)

where \(E,\) is the energy, is the mass \(m,\) and \(c,\) is the velocity of light in vacuum.

Chemical Energy

Atoms are connected to other atoms in bonds. The bonds that connect these atoms are due to chemical energy. This stored chemical energy is released during a chemical reaction. Usually, this is converted to heat energy.

Chemical energy is found in food, wood, fuels such as coal, petroleum, natural gas.

Light Energy

This is the energy that can be sensed by the eyes of animals. It is made of energy packets called photons that travel in waves. It is an electromagnetic wave.

Heat Energy

It is also called thermal energy. All matter is made of atoms. The atoms vibrate within the available space for them. If they move faster, it means they have more thermal energy making those objects hot. A cold object such as ice does not mean it does not have heat energy, it only means the molecules in it vibrate very slowly, giving out less heat.

Electrical Energy

It is a form of energy caused by moving charges called electrons. This movement of charges is called electric current. Electric energy is used to run different electric appliances we use in our daily life.

Sound Energy

It is the movement of energy through a medium in the form of waves. When an object vibrates, the energy is transferred in the form of waves. There are certain frequencies of waves that the human ear can sense. This vibration is sensed by our ears as sound.

Law of Conservation of Energy

According to the Law of Conservation of Energy, Energy can neither be created nor destroyed.

It can change from one form to another. This means that total energy remains constant. As we have learned from the mechanical energy section, the potential energy of a stone converts to kinetic energy when it starts rolling downhill.

Let us see a few examples of the conversion of energy from one form to another.

1. Chemical to Heat and Muscular

The food consumed by humans and animals has chemical energy. After digestion, this gets converted to heat that keeps the body warm. It is also converted to muscular energy needed for various functions and movements of the body. This is also necessary to keep all our organs running in good condition. When we do our daily activities, the energy gets converted to these forms and so, we feel tired. So, all organisms need food to sustain themselves.

There are certain types of foods that give instant energy, such as sugars. Therefore, athletes are provided with energy drinks and glucose. Certain foods such as fats store energy and release it to the body slowly.

2. Chemical to Electrical

This is another example of using chemical energy. The battery cell has chemical energy that gets converted to electrical energy. Electrical energy can be converted to most other forms, such as light in lamps, mechanical energy in motors, fans and pumps, and sound energy using a speaker.

Charging of a battery cell is the reverse process where electrical energy is converted to chemical energy and stored in it.

Photosynthesis is a process of converting the light energy of the sun into chemical energy by the leaves of plants

3. Mechanical to Electrical

Water falling from a height means conversion of potential energy to kinetic energy. This combined form of what we call mechanical energy turns a water wheel or turbine. The turbine is connected to a generator that creates electrical energy.

Wind energy is a form of mechanical energy due to wind pressure (potential energy) and its movement (kinetic energy). This energy can rotate the blades or fans of windmills. Windmills have generators inside to them to convert this rotation into electrical energy.

4. Nuclear to Electrical

The nuclear energy in the nucleus of atoms is used to obtain electrical energy. Fission or fusion creates heat energy. When this heat is used to boil water, steam is generated that turns the turbines to generate electricity.

Renewable and Nonrenewable Sources of Energy

The important thing to be noted when using these words is the word ‘sources’. According to the laws of conservation of energy, energy cannot be created or destroyed. So, we are not talking about energy, but sources of it.

Renewable Source

In simple words, this source can be used continuously and everlastingly to get the same type of energy. Solar energy, wind energy, ocean wave energy, tidal energy, hydel energy, geothermal energy are a few of these sources. These sources do not get used up during the conversion of energy.

Nonrenewable Source

During the conversion of one form to another, if the first form is used up never to get back, then it is a nonrenewable source. Usually, most chemical sources are nonrenewable. Firewood, fossil fuels such as coal, petroleum, natural gas are nonrenewable sources. Once burnt, we never get them back in their original form.

Conservation of Energy Sources

When energy cannot be created or destroyed, what is there to conserve? The answer to this question is closely related to the above topic, renewable and nonrenewable. The world is using up fossil fuels quickly and it will run out in the coming years.

Two ways of conservation of nonrenewable sources are:

1. Using them as judiciously as possible, such as cycling to nearby places, using carpooling, switching off the engine at long traffic signals.
2. Using renewable sources such as solar power for heating water, charging batteries, and lighting up homes, using biogas for cooking are a few of the solutions.

Interesting Fact About Energy and Mass

The sun loses about \(700\) million tons of its mass every second. In one second, this amount of Hydrogen is lost by conversion to energy in the fusion process of converting to Helium.

Energy – Sample Problems

Q.1. The rock of \(10\;{\rm{kg}}\) is moving with a speed of \(10\;{\rm{m}}\,{{\rm{s}}^{ – 1}}.\) What is its kinetic energy?
Sol:
Velocity of the rock \(v = 10\;{\rm{m}}\,{{\rm{s}}^{ – 1}}.\)
Mass of the rock \(m = 10\;{\rm{kg}}\)
Kinetic energy \(\;KE = \frac{1}{2}\; {\rm{m}}{{\rm{v}}^2}\)
\(\Rightarrow KE = 12 \times 10 \times {10^2} = 500\,{\rm{J}}\)

Q.2. A rock of \({\rm{10\;kg}}\) falls from a height of \({\rm{100\;m}}\) from rest. What is its kinetic energy just before it touches the ground?
Sol:
Mass of the rock \(m = 10\;{\rm{kg}}\)
Height through which it is falling \(h = 100\,{\rm{m}}\;\)
Initial velocity \(u = 0\)
From the conservation of mechanical energy, mechanical energy at the topmost point and at the bottom most point must be same.
\(K{E_1} + P{E_1} = K{E_2} + P{E_2}\)
\(\Rightarrow \frac{1}{2}m{u^2} + mgh = \frac{1}{2}\,{\rm{m}}{{\rm{v}}^2} + mg\left( 0 \right)\)
\(\Rightarrow \frac{1}{2} \times 10 \times {0^2} + 10 \times 9.8 \times 100 = \frac{1}{2} \times 10 \times {v^2} + 0\)
\(\Rightarrow v = 44.27\;{\rm{m\;}}{{\rm{s}}^{ – 1}}\)

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We hope that this article covering the topic of Energy has helped you in understanding the concept in detail.