# Work and Energy

## Table of Contents

## Law of Conservation of Energy

According to Law of conservation of energy; energy can neither be created nor be destroyed rather the form of energy can be converted from one form to another form.

Law of conservation of Energy states that the total energy of a system remains unchanged before and after transformation.

**Example:** When an object having potential energy is dropped from a height, the potential energy is changed into kinetic energy.

The sum of potential energy and kinetic energy remains constant at every point of the falling of object.

i.e. `mgh +1/2mv^2 `= constant at every point

The sum of potential energy and kinetic energy is the total mechanical energy of the object falling from a height.

During free fall of the object, the potential energy starts decreasing and converting into kinetic energy with decrease of height from the ground.

### Various Forms of Energies are convertible

One form of energy can be converted into other form.

**Example:**

- Heat energy is converted into electrical energy in thermal power stations.
- Electrical energy is converted using an electric bulb into light energy.
- Electrical energy is converted into heat energy using an electric heater.
- Chemical energy is converted into electrical energy using an electric cell.

## Power

Rate of doing work is called power. For example; a more powerful engine can do more work in less time, such as an aero plane covers more distance in less time than a car consequently aero plane is more powerful than a car.

Since power is the rate of doing work

∴ `text{Power} = (text{Work})/(text{Time})`

`=>P = W/t`

Where, ‘P’ is power, ‘W’ is work done, and ‘t’ is time taken in work done.

### SI unit of power

The SI unit of work done is joule

SI unit of time is second.

Therefore, SI unit of power is equal to joule per second or Js ^{– 1}.

The SI unit of power is watt named after James Watt, the inventor of steam engine, and is denoted by ‘W’.

1 W = 1 J s^{ –1}

The bigger unit of power is kilo watt and is written as kW.

1 kilowatt = 1000 watt

Or, 1 kW = 1000 W

Or, 1kW = 1000 J s^{ –1}

The average power can be calculated after dividing total work done by total time taken.

### Commercial Unit of Energy

Since joule is very small thus, large quantity of energy is expressed in kilo watt hour and is written as kWh.

If a machine uses 1000 joule of energy in one second and the machine runs for one hour, then it is said that the machine will consume energy 1kWh.

1 kWh = 1 kW x 1 h

Or, 1kWh = 1000 joule x 3600 s

Or, 1 kWh = 3600000 joule

Or, 1kWh = 3.6 x 10^{6 }joule

Electric consumption in households is measured in kWh and generally called unit. Therefore, 1 unit of electricity is equal to 1kWh.

Energy = Power X time

Thus, by knowing any two of three, third can be calculated using the expression Energy = power x time.

If an electric appliance consumes 1000 joule of energy in one second and runs for one hour, it will consume 1unit of electricity, i.e. 1kWh of electricity.