Have you ever wondered why do we start to rub our hands together the moment we start to feel a bit cold? You know the answer, don’t you? That action heats up your hands and gives you a little bit of comfort in that particular situation. But did you ever think about the mechanics behind it? Well, here’s the explanation.

When we rub our hands together, we use mechanical energy to create friction that generates heat energy. As you may realize, the heat does not just appear out of nowhere. You are basically turning the mechanical energy into heat energy. This is an application of the law of conservation of energy, which is one of the fundamental concepts in Physics.

According to this law, energy cannot be created or destroyed. However, changing the form of energy is possible, exactly the way we warm our hands. Well, rubbing your hands to generate heat is only a simple application of the law. It has been in practice since the beginning of time, and you will find more than one application of this law at every step of our daily routine.

So what is the law of conservation of energy?

As you may realize, the term “conservation” refers to the principle by which the total value of a particular physical quantity or parameter remains unchanged within a system, unless the system is subject to external influence.

By that definition, the conservation of energy means that the amount of energy within a system will remain unaltered over time. The proper definition of the law of conversation of energy is this,- “Energy can neither be created nor destroyed. It can only be converted from one form of energy to another.”

There are several examples that can simplify the concept for you:-

When you switch on the fan in your bedroom, the electrical energy gets converted into the mechanical energy. Similarly, when you switch on a bulb, the electrical energy that flows within the wire gets converted into light and heat energy.

The green plants use sunlight to carry out the photosynthesis process. It allows them to store the energy in their cells. In this process, the light energy is converted into chemical energy which they use for their growth and nourishment.

In thermal power stations, the heat energy is converted to electrical energy. The heat, however, is generated from the combustion of fossil fuel, which is a transformation of chemical energy into heat energy.

When you stop a ball from rolling on the floor, it may seem like there’s no conversion of energy, but in reality, you absorb the kinetic energy of the ball and turn it into heat potential energy.

Even when you are pushing a chair to move it from its static position, you are using the potential energy stored in your body to do the task. At first, your potential energy gets transferred to the chair. Then it is converted into kinetic energy, which finally makes the chair move from its position.

Basically, we are witnessing the conversion of energy every minute, and if we do the math and calculate how much energy is converted in each process, we will find that the total amount of energy within the system remains the same. However, it is important to understand what “system” means in this context.

What does “system” mean in the context of “conversion of energy”?

A system can mean a lot of things in science, but to give the term a general outline, it can be said any collection of objects that we choose to model with our calculations is a system. When the matter of “conversion of energy” is involved, a system generally involves the object of interest and anything that interacts with it.

However, in practice, physicists often ignore some interactions while outlining a system for their convenience. Usually, the things that are excluded from the “system” are collectively termed as the “environment”.

Even though ignoring some part of the environment will make the calculations less accurate, but the physicists continue to ignore several aspects of the “environment” while working on their hypotheses. Generally, a physicist is considered as a good one when he is able to identify which element of the “environment” is going to be crucial for the equation and which can be ignored safely.

For instance, in case of air rifle shooting, the objects of interest are the rifle, the bullet and the target. But if you need to be more specific, you need to include Earth's gravitation pull as well which has an influence on the motion if the bullet. One can even go further and add the wind to the system as well. However, if the shooting is held in a short range, the wind factor can be ignored safely. In shorter range, the air resistance won't have much of an effect the motion of the bullet.

Now that you have a decent idea about the law of conservation of energy and the concept of “system”, we can proceed to the part we discuss the law of conservation of energy formula.

The formula of conservation of energy:

An object (or multiple objects) in a closed system can have both kinetic and potential energy. The total energy in that system, which is the sum of the kinetic and potential energy, is termed as total mechanical energy. As mentioned earlier, if the system is not subject to external influence, the total mechanical energy remains conserved.

The kinetic energy can change into potential energy and vice versa without altering the total energy with the system. However, when the mechanical system is not fully closed, external influence can change in the total mechanical energy. The system can perform "work" in the surroundings, or some "work" can be done on the system. This other work is often considered as the external influence.

The following equation explains how the whole thing is measured:

K1 + U1 + W = K2 + U2

In this conservation of energy equation, K1 denotes the initial kinetic energy in the system while U1 indicates the initial potential energy. W is the amount of external influence or work that was done on/by the system. K2 and U2 are the final kinetic energy and the final potential energy respectively.

Interestingly, the conservation of energy also outlines the first law of Thermodynamics. It states that the change in internal energy of a system is equal to the difference of the heat transfer into the system and the work done by the system. The first law of thermodynamics is often explained by the following equation:

ΔU = Q – W

In this equation, ΔU denotes the change in the internal energy, while Q denotes the heat transfer into the system and W the work done by the system respectively. While this particular law of Thermodynamics is an application of the conservation of energy, there is another famous formula in the field of Physics that talked about something on the similar line.

E = mc^2

This formula of mass-energy equivalence, which was discovered by Albert Einstein, identifies the mass of an object as a form of energy. Mass and energy – these two fundamental quantities relate to each other as per the formula mentioned above. Here, E signifies energy while m denotes mass and c stands of the speed of light (3 x 10^8 m/s). This brings us to the parallel concept of conservation of mass.

What is the law of conservation of mass?

Interestingly, the law of conservation of mass was discovered by Antoine Lavoisier in 1785, 57 years before the law of conservation of energy by Julius Robert Mayer. However, there’s no harm in learning about conservation of energy before the conservation of mass.

If you are looking for the law of conservation of mass definition, all you need to do is repeat the law of conservation of energy definition and replace “energy” with “mass” in the statement. The law of conservation of matter (mass) states that in a closed or isolated system, matter cannot be created or destroyed. It can only change its form.

If you burn a candle in a properly sealed room, where nothing (not even air) can come in or get out, you will find that some of the melted wax gets deposited at the bottom of the candle while some portion of the wax disappears as the flame goes down the wick. So, you may wonder, how does the matter is conserved within the enclosed system?

Well, even when you see some of the wax disappear, it still complies with the law of conservation of mass. As the candle burns, the heat melts some portion of the wax while a certain portion of it gets converted.

Due to the combustion, the oxygen in the room reacts with the candle wax and produce water vapor (H2O) and carbon dioxide (CO2). If you calculate the total mass of the objects including the constituent components in the air, you will see the result is same as it was before you lit the candle.

Einstein’s mass-energy relation:

In the year 1905, Einstein changed the perception of people reading the concept of mass with his theory of relativity. He established the fact that mass is not absolute. It can be converted into energy and increase significantly at exceedingly high speeds near that of light.

According to Einstein’s equation of mass-energy equivalence, the total energy of an object comprises of its rest mass and the increase of mass caused by high speed. For any atomic or chemical reaction, some conversion between rest mass and the energy takes place. This is why the products of a reaction process usually have a smaller or greater amount of mass than the reactants.

This brings us to the idea of conservation of mass-energy. It suggests that the mass and energy associated with the object (or objects) within an isolated system remain unchanged in quantity. Though, these elements (mass and energy) can be converted into one another within the system.

During the event of nuclear fission or nuclear fusion, some mass of the nucleus turns into a massive amount of energy. This explains why a certain amount of mass goes missing from the total mass of the original particles once the event is completed. The binding of nuclei generates massive energy which is used in nuclear power plants and often as nuclear weapons.

Over the years, Physicists have studied the laws of conservation of energy and mass, and have tried perfect the concept with valuable inputs. In fact, some of them have been able to make some crucial discoveries in this area. Niels Bohr and Wolfgang Pauli are two noteworthy names who have worked on the areas related to the conservation of mass and energy.

The application of the law revolving conservation of mass is quite popular in the field of Chemistry. Since the change in energy in a chemical reaction is so little that it does not affect the measurements. However, with some recent innovations, it is now possible to accurately measure even a tiny amount of change within an isolated system.

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