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# Law of Conservation of Energy

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 Sub Topics Energy may change from one form to another and does so without a net loss or net gain. That is so say, energy is conserved, and the total amount remains constant. The study of energy transformations has led to one of the most basic scientific principles, the law of conservation of energy.Although the meaning is the same, the law of conservation of energy or simply the conservation of energy can be explained in different ways.

## What is the Law of Conservation of Energy?

What is law of conservation of energy?

The law of conservation of energy states that "energy can be neither created nor destroyed and expresses the fact that the total amount of energy remains constant as it changes from one form to another." This law is one of the cornerstones of science and helps us to develop a better understanding of the world around us.

Although this law applies to the energy exchanges that occur in sports and exercise in practice its application is rather limited because the possible energy combinations are too numerous, but a more restricted form of the law can be identified that does have value.

## Different Forms of Energy

The analysis of energy flow is complicated because energy takes on several different forms. Kinetic, potential, thermal and radiant energy all play important roles in chemistry. Working with energy at the molecular level requires a molecular perspective and an understanding of energy flow.

What are different forms of energy?
1. Any moving object possesses energy of motion, which is called kinetic energy. Kinetic energy varies with the mass of the body and the speed at which it is moving.
2. An object at rest has no kinetic energy. However motionless objects frequently possess a form of stored energy known as Potential energy. For example, a rock teetering high on a ledge is about to release stored gravitational energy, a cloud on the verge of "hurling" a thunderbolt earthward is about to release stored electrical energy, and gasoline in the cylinder of an automobile engine is about to release stored chemical energy. In each case, the stored energy is called potential energy.
3. Temperature rises whenever a body loses kinetic energy without gaining potential energy. When a catcher catches a fastball, the kinetic energy lost by the ball shows up as thermal energy of the glove and the ball. A change in Thermal energy results in a temperature change. If a system gains thermal energy its temperature increases if a system loses thermal energy its temperature decreases.
4. Another important form of energy also plays a fundamental role in chemistry. The temperature of an object increases when it is placed in direct sunlight because light posses energy. This energy is called Radiant energy. The radiant energy absorbed by an object is converted to thermal energy, thus there is increase in temperature.
Different forms of energy is given in joules.

## Free Falling Object

The Italian Galileo originated our present ideas concerning falling objects. When we use the expression freely falling object, we do not necessarily refer to an object dropped from rest.

A freely falling object is any object moving freely under the influence of gravity alone, regardless of its initial motion. Objects thrown upward or downward and those released from rest are all falling freely once they are released.

Any freely falling object experiences an acceleration directed downward regardless of its initial motion.

## Law of Conservation of Energy Definition

Numerous experiments are performed to define law of conservation of energy and experiments have shown that energy is neither gained nor lost during physical or chemical changes. This principle is known as the law of conservation of energy and is often stated as follows.

Definition of law of conservation of energy:

"Energy is neither created nor destroyed in ordinary physical and chemical changes. If the system under study loses energy (the reaction is exothermic and $\Delta$H is negative), the surroundings of the system must gain the energy that the system loses so that energy is conserved."

## The Law of Conservation of Energy States That

To state the law of conservation of energy is that "energy cannot be created or destroyed, but that energy can only be changes from one form to another."

## Law of Conservation of Mass and Energy

Einstein formulated the law of conservation of mass and energy, which states that mass and energy are interchangeable under special conditions. The conditions have been created in nuclear reactors and accelerators, and the laws has been verified.

This relationship can be expressed by Einstein's famous equation.

E = mc2
Energy = Mass $\times$ (velocity of light)2

## Law of Conservation of Matter and Energy

Two basic laws that emerged early in the history of science are the law of conservation of matter and the law of conservation of energy.
1. The first of these laws simply states that within the universe as a whole, matter cannot be created or destroyed.
2. The second law says the same thing with respect to energy.

Not long after Marie and Pierre Curie in 1898 isolated two radioactive elements, polonium and radium, scientists were forced to conclude that matter can be transformed into it became necessary to combine that two laws into a single law of conservation of matter and energy: The sum total of all matter and energy in the universe must remain constant.

## Law of Conservation of Mechanical Energy

The specific form of the law of conservation of energy which has the property of perfect energy exchange between its components is referred to as the conservation of mechanical energy.
This refers to exchanges between just two types of energy the gravitational potential energy and kinetic energy and is given by the equation. The total mechanical energy is always a constant.

In general the conservation of mechanical energy applies to projectile light where air resistance can be neglected. It cannot be applied where there are obvious energy losses due to friction or other resistances.

## Examples of Law of Conservation of Energy

Energy conservation processes often produce heat as a bye product. The example of law of conservation of energy is when a ball is dropped it is compressed as it hits the ground and after the recoil never quite reaches the same height from which it was dropped. This failure to regain the original drop height is due to a lose of energy as a result of the compression and is indicative of the efficiency of energy conversion which, if heat is generated, is always less than 100%.

If that compression were repeated many times the ball would warm up, a characteristic which is used to good effect in the game of squash where the warm ball rebounds with greater speed than a cold ball.

## Law of Conservation of Energy Equation

According to law of conservation of energy the principle of energy is based entirely on experience. The first law of thermodynamics is merely one statement of this principle with reference to heat energy and mechanical energy. The conservation of energy equation is given by

dE = $\delta$Q- $\delta$W

Where Q and W are determined on the basis of rate equation. The rate equation is written as
$\frac{dE}{dT}$ = $\delta$Q - $\delta$W
$\frac{d}{dt}\int_{system} edm$ = $\delta$Q - $\delta$W

Where Q and W are the rates of heat and work transfer from the total mass of the system and e is the total stored energy per unit mass. The law of conservation of energy formula for a system is written as

$\frac{\partial }{\partial t}(E)_{sys} = Q - W$

## Explain the Law of Conservation of Energy

One of the most fundamental laws of the nature is the conservation of energy. The following examples are taken to describe the law of conservation of energy.
1. The rock falling of a cliff. It picks up speed as a result of potential energy being converted into kinetic energy.
2. A brake is applied to a moving automobile. The kinetic energy of automobile is converted into heat energy through friction.
3. A current passing through electrical heater. Th electrical energy is converted into heat energy.
4. A person who has a greater diet that is energy input than energy output will gain weight and a person who has less energy input than output will loose weight.
The above examples show that one form of energy is simply converted into another form and there is no change in the total energy of the system and surroundings.

## Law of Conservation of Energy Problems

Solved problems based on the concept law of conservation of energy is given below.

### Solved Examples

Question 1: The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? why?
Solution:

During the free fall of the object, there is continuous decrease in potential energy. This decrease in potential energy, appears as an equal of increase in kinetic energy. Thus the sum of the potential energy and kinetic energy of the object would be the same at all points. That is

Potential energy  + kinetic energy = Constant

According to the law of conservation of energy, the total energy of system remains unchanged. Thus the given statement does not violate the law of conservation of energy.

Question 2: An electric heater is rated 1500W. How much energy does it use in 10hours?
Solution:

Power of an electric heater P = 1500W = 1.5kW
Time taken, t = 10h

Energy = Power $\times$ Time taken
Energy = 1.5kW $\times$ 10h = 15kWh = 15units

The energy consumed by the heater is 15 units.