Conservation of energy

Energy is associated with all natural phenomena as well as with many topics in public discussions. All production and actually the whole global economy depend on energy. Being able to consume energy, that there are enough energy resources available at reasonable cost, is vital for mankind.

In natural phenomena energy is stored, transmitted and converted. There is convection of energy in moving liquids and gases. Moving solid bodies as well as waves carry energy. Electromagnetic radiation carries energy and heat is conducted from higher temperature to lower temperature. However, the total amount of energy is conserved in all phenomena. Energy is not created, neither it can disappear. This is the principle of conservation of energy covering all natural phenomena under normal conditions.

The principle of conservation of energy: Energy can neither be created nor destroyed.

Energy can be converted from one form to another, but a planned conversion process is sometimes easy, sometimes difficult or even impossible. Energy forms which are easy to convert to other forms of energy are sometimes classified as free energy. Free energy can easily be utilized in running useful processes. Such energy forms include kinetic energy, radiation energy and heat. Confined energy is stored in one way or another and it must be set free before it can be utilized. For instance, food contains chemical energy which is converted in digestion processes to thermal and mechanical energy. Mechanical energy is either kinetic or potential energy. These energy forms alternate for instance in a pendulum or a swing.

Conversion of energy from one form to another can be visualized using an energy diagram. In such a diagram there are two sections presenting the quantities of different types of energy in the beginning (left) and at the end (right) state of the process. Energy conversion processes are illustrated by arrows. The principle of energy conservation is illustrated by the sections being of equal height.

Energy conversion when an apple falls from a tree.

Green plants can convert solar radiation energy in photosynthesis processes partially to chemical energy. Simultaneously some radiation energy is absorbed in plants as heat.

In photosynthesis solar radiation is converted and stored as chemical energy.

In burning processes chemical energy is converted to heat (thermal energy) and light which will ultimately return as radiation to outer space.

Chemical energy is converted to light and heat when burning firewood.

When lifting an apple some chemical energy stored in muscles is converted to potential energy of the apple. Having potential energy means that a body has more energy than when being on ground level. Thus it could for instance drop down and get kinetic energy. We indicate in the first section of the energy diagram the initial chemical energy stored in the muscles and in the final section the potential energy of the apple. In the arrow indicating the process we write “lift” describing what we have done.

When lifting an apple chemical energy stored in muscles is converted to potential energy of the apple.

When you push or pull a body the contact interaction conveys energy from you to the body. The work done by you (the force multiplied by the distance the body moved) indicates how much energy was conveyed.


Kinetic energy

When you kick a simple scooter for higher speed (on flat surface), chemical energy in your muscles is converted to kinetic energy of the scooter and yourself as well as to heat while winning friction and other resisting forces. When the scooter is moving, friction in scooter bearings, air resistance and other resisting forces work for slowing down the movement. Energy has to be conveyed all the time by kicking continuously to overcome these forces if you wish to maintain speed. Scooter bearings, pavement and surrounding air are heated although it is not usually easy to observe or measure.

If you have two people riding a tandem scooter, you have to use much more chemical energy stored in muscles to achieve the same speed since you have heavier mass to move. Also, if you wish higher speed you have to use more energy.

A moving body has kinetic energy depending on its mass and speed.

Human beings get the energy they need from their food. For instance chemical energy stored in an apple is used and converted to kinetic energy when walking.

Potential energy

A parachutist is brought up to high altitude by an aeroplane to let him jump down. The aeroplane uses chemical energy stored in fuel and converts it in its engines to mechanical energy to gain speed and altitude. Consequently, a part of the used chemical energy has been converted to the potential energy of the parachutist. This potential energy depends on the mass of the parachutist and the altitude. When the parachutist jumps from the plane, his potential energy begins to be converted to kinetic energy and partly also to heat due to air resistance. Air resistance grows rapidly with higher speed so the parachutist will soon descend in constant speed. Strong air turbulence caused by the falling parachutist with his parachute heats air. You may relate this warming due to frictional forces to the feeling of warmth when you rub your hands together. In this process of falling potential energy is converted to thermal energy. However, heat does not cause noticeable warming of air or parachutist.

Potential energy of a body is stored energy which can later be used for different purposes and its magnitude depends on its mass and location (altitude).

When an apple falls down its potential energy is converted to kinetic energy.

Chemical energy

When you lift something, say an apple, your muscles work. Muscles take the energy they need from food. In food energy is stored as chemical energy, which is converted in human digestion processes and muscular functions to activities like breathing, moving and lifting. We speak of energy stored and used by muscles.

Plants use photosynthesis to assimilate solar radiation energy. In photosynthesis carbon dioxide in air and water in soil are brought together to react and form sugar. Thus solar energy is stored in chemical compounds in plants. When a plant, for instance firewood is burned, this stored chemical energy is converted to heat. In burning reactions the original compounds carbon dioxide and water are again formed.

Chemical energy is stored in chemical compounds. Such compounds are found for instance in plants, muscles, oil, coal and electric batteries.


Investigations on different forms of energy

Mechanical energy

Investigation 1.
Kinetic energy of marbles.

- marbles of different sizes
- a wooden block or a matchbox
- a piece of paper

Roll a marble-size tube of the piece of paper and use it for directing marbles through it to hit the target. Set a marble to roll through the tube on floor. Regulate marble speed by varying the inclination of the tube and the initial height of the marble.

Put the wooden block on the floor. Roll a marble slowly to hit the block.
What you observe?
Explain the reasons for your observations.

Take a bigger (heavier) marble and repeat the previous experiment.
What you observe?
Explain the reasons for your observations.

Investigation 2. Potential energy of marbles

- marbles of different sizes
- wooden or paper balls of similar sizes
- water in a bowl

Drop a marble to water from different heights.
What you observe?
Explain the reasons for your observations.

Drop a marble and a wooden or paper ball of the same size to water from the same height.
What you observe?
Explain the reasons for your observations.


Chemical and electric energy and light

Potato as light source


- 3-5 raw potatoes
- zinc nails
- copper nails
- leads with crocodile connectors
- low-voltage LEDs (1.7-1.9V)

LED (Light Emitting Diode) is a semiconductor component, emitting light when there is an electric current through it. They use much less energy than incandescent lamps. They are used nowadays for numerous purposes in electronic devices etc. They can be used for a very long time.

1. Put zinc and copper nails in the potatoes as in the figure above and put three potatoes in a row. Connect the copper nail of the middle potato to the zinc nail of an outer potato and the zinc nail of the middle potato to the copper nail of the other outer potato. Connect the “free” nails of the outer potatoes to the “feet” of a LED. If the LED does not lit, change the connecting leads with each other. If there is no light even now, add one potato similarly and try again.

- make a drawing of your circuit and explain what you observe.

Could you replace potatoes with something else? Try to get a led glowing.

2. Experiment trying to find out the reasons for getting higher or lower voltages in different types of cells and batteries. You need here voltmeters, ammeters, nails or wires of different metals, roots, fruits etc.
- Find out when you get the highest voltage.
- Find out when you get no voltage.


13. What common features and what differences have accumulators/chargeable batteries and common dry cells/batteries.

14. Write a list of appliances where there is an inner voltage.

15. Explain, where in the figure below there is a) voltage, b)current. Which is the reason, which is the outcome?


Mechanical and thermal energy

Investigation 1. Thermal energy from mechanical and chemical energy

Rub your hands together. Clap your hands. How the chemical energy stored in your muscles is converted?

Raise yourselves standing on a chair.
Explain, how the chemical energy stored in your muscles is converted now?

Step up on the chair and jump down fast 20 times in a row.
Explain, how the chemical energy stored in your muscles is converted in this case?


Conservation of energy in everyday phenomena

Energy transmission by electric current

Much of the energy consumed at home, in school as well as in business and industry is in the form of electric energy. Electric energy transmission is economical even over long distances. High-voltage transmission lines do not waste a high percentage of energy. Thus it is possible to locate big thermal power plants at remote areas and use transmission lines to give consumers access to energy resources. This is often important for environmental reasons and for safety (especially for nuclear power plants and plants using coal).

Transmission and conversion of electric energy are commonplace even in small scale everyday phenomena. An electric battery and a small electric bulb form a simple electric circuit in a torch. The bulb is actually a small incandescent lamp and when glowing, it converts about 93% of electric energy to heat and only 7% to light. The energy is taken from the chemical energy stored in the battery.

Draw an energy diagram of the closed electric circuit formed by the bulb and the battery:

1. The battery provides energy to the electric circuit. The source of this energy is chemical reactions in the battery.
2. When glowing, the bulb produces light and heat.
3. An arrow in the energy diagram indicates the transmission of energy by electric current.

Kinetic energy of a car

An old-fashioned car is often as heavy as a modern race car. However, a race car has much higher maximum speed and thus it has a much higher maximum kinetic energy.

Hydroelectric power

Hydroelectric power is based on the potential energy of water running down from mountains, hills and reservoirs. The higher the drop the more kinetic energy water has when hitting the blades of a turbine. A water turbine may rotate at very high speed and it again runs a generator. The generator is the source of electric current.


Wind energy

Energy production in a wind energy mill is based on utilization of the kinetic energy of blowing wind.

Producing electricity in a thermal power plant

In a thermal power plant fuel like coal, oil, natural gas or peat is burned to heat and boil water. Produced steam is led to a turbine which runs a generator producing electricity.

The principle of a nuclear power plant is similar, but the source of heat is in nuclear reactions. Uranium nuclei are split in fission processes when hit by neutrons. These processes produce much heat, which is used to boil water.

Meteorites meet friction in atmosphere

Friction heats moving bodies. When a meteorite hits outer layers of our atmosphere, it looses kinetic energy due to air resistance. Friction forces heat it to such a high temperature that it will glow. The light emitted by the glowing meteorite is seen as a falling star.

Energy in food vs. consumption

The unit of energy is joule (1J). It is a rather small unit, thus we often use kilojoule (1kJ=1000J).

Food has stored chemical energy in it. In the following we list food portions having energy content of approximately 400kJ.

1 cup of coffee with sugar and cream
2 spoonfuls of sugar
1 fried egg
1 large glass of full milk
35 grams of cheese
1 large cup of Coke
1 chocolate bar
50 grams of beef
6 potato chips
5 pieces of French fries
1 portion of ice cream

Correspondingly, energy consumption in the following activities for 30 minutes is:

slow cross-country skiing 1400kJ
playing soccer 1100kJ
rowing 1500kJ
biking 1100kJ
swimming (crawl) 1700kJ
jogging 1400kJ
walking 600kJ


History of the concept of energy

Energy as a scientific concept is the outcome of a development over several centuries. Galileo Galilei studied movement of bodies in 16th century and through experimenting entered at a principle of conservation of mechanical energy. This principle indicates that when a body moves under gravitation, it has kinetic energy and potential energy in variable amounts transforming one to another, but their sum, the total energy is conserved.

Heat is historically the second starting point of energy studies. Englishman Brook Taylor studied in the beginning of 18th century how temperature changes when mixing liquids initially at different temperatures. Scotchman Joseph Black interpreted Taylor’s results stating in 1760s that the amount of heat is conserved in thermal phenomena and that each substance has a typical specific heat capacity.

Movement and thermal phenomena were at first studied separately as they were not supposed to have any connection. However, Julius Mayer from Germany published in 1842 the principle of conservation of energy including both mechanical and thermal energy. James Joule (an Englishman) studied thoroughly the equivalence of mechanical and thermal energies in 1840s. This energy conservation principle is thereafter often known as Joule’s law.

Later chemical and electromagnetic energy forms were included in the principle of energy conservation. The general principle of energy conservation covering all forms of energy was first published by Hermann von Helmholtz (German) in 1847.

When we take into account the atomic structure of matter, we may formulate new unifying ideas: heat (thermal energy) can be interpreted as kinetic energy of atoms and molecules. Chemical energy is interpreted as potential energy of atoms in mutual interaction and similarly nuclear energy is potential energy of elementary particles within nuclei. However, the principle of conservation of energy remains the same: the sum of all energy forms does not change.

A significant addition to the concept of energy was introduced by Albert Einstein (German/Swiss/American) in his special theory of relativity in 1905. This theory states that mass and energy relate to each other according to the formula E=mc2. Thus the total mass-energy of a body consists of its mass at rest, its kinetic energy and the sum of its potential energy in all relevant interactions. The generalized principle of conservation states that this mass-energy is conserved.


1. Draw energy diagrams illustrating energy transmission and conversion in the following situations:
a. A pencil falls down on floor from a table.
b. A bag is lifted on a table.
c. Water is boiled in a kettle.
d. A candle is burning on a table.
e. You rub your hands together.
2. Find out the path of energy from the sun to thermal energy of tea in a teacup. Draw an energy diagram illustrating the process.
3. Describe natural phenomena where energy is a) stored and b) released. Illustrate these phenomena using an energy diagram.
4. Discuss when in everyday situations you have (your body has) kinetic energy and/or potential energy.