## Blog

# Chapter 2.1 Energy and Its Units Explained – Solar

- April 13, 2023
- Posted by: iisemumbai
- Category: Learning Resources

**2.1.5 Energy and Its Units**

‘Energy’ as quantity can be represented in several units. One of the basic units of energy is called ‘joule’ and it is abbreviated as ‘J’. One joule of energy is equal to energy expended (or work done) in applying a force of one newton through a distance of one meter. In terms of electrical energy, one joule energy is equal to energy expended in 1 watt of power running for 1 second. One joule represents a very small amount of energy. For instance, energy consumed by a 100 watt bulb in one hour is 360000 joules. The energy content of the food that a normal person eats daily is about 10000 joules.

Other than joules, there are many other units of energy that we usually hear in our daily context. The other energy** **units normally represent higher amount of energy. For instance, energy content of food is given in terms of calorie and one calorie represents 4.182 joule of energy. Our monthly electricity bill is given in terms of number of electrical energy units consumed by us. One ‘electrical energy unit’ is equal to 1 kilo-watt-hour (or kWh) and 1 kWh represents 3,600,000 joules of energy. The energy content of a metric ton of crude oil is given in term of Tons of Oil equivalent (ToE).

*Unit conversion factors *

The different energy units are related with each other through different constants. Table 2.2 gives relationship between different energy units. Normally, in order to represent larger units, prefix are added to the unit. For instance, joule is a small amount of energy in term of joule only prefix ‘kilo’ which represents 1000 is added to make 1000 joules or 1 kJ. This is similar to write 1000 grams of weight as 1 kg. Similarly , prefix ‘mega’, which represents 1000,000 (or 1 million) is added to make it 1000000 joules or 1 MJ. Also, if we multiply 1 MJ with 1000, we will get 1000 MJ. In brief, 1000 MJ is written as 1 giga joule or 1 GJ. Here, giga represents 1,000,000,000 or 1000 million.

One can notice from the above discussion that 1 kJ is 1000 times larger energy than 1 J, 1 MJ is 1000 times larger energy than 1 MJ. This can be represented in the following way :

1 kJ = 1000 J

1 MJ = 100 kJ

1 GJ = 1000 MJ

This conversion factors are not used only in application to energy units, but they are also used in the application to other units like unit of power (watt or W). Applying these unit conversion factors to power unit we will get ; W, kW, MW, and GW.

Some commonly used prefix and conversion among them is given in Table 2.2.

**Table 2.2** Commonly used Prefix, Their value and Symbols for Representing Large Values

Prefix | Value of Prefix | Alternate way of writing prefix | Symbol | Example |

Kilo | 1000 | 103 | K | 1 kg = 1000 grams |

1 kJ = 1000 joule | ||||

Mega | 1,000,000 | 106 | M | 1 MJ = 1,000,000 J |

1 MJ = 1,000 kJ | ||||

Giga | 1,000,000,000 | 109 | G | 1 GJ = 1000 MJ |

1 GJ = 1,000,000,000 J | ||||

Tera | 1,000,000,000,000 | 1012 | T | 1 GJ = 1,000,000,000,000 J |

Peta | 1,000,000,000,000,000 | 1015 | P | 1 PJ = 1,000,000,000,000,000 J |

Exa | 1,000,000,000,000,000,000 | 1018 | E | 1 EJ = 1,000,000,000,000,000,000 J |

*Various Units of Electrical Energy *

In this training manual, we are mainly concerned with electrical energy. One joule of electrical energy is equal to energy expended in 1 watt of power in duration of 1 second. From the above discussion, we can write the following expression for energy :

Energy (joule) = Power (watt) X Time (Second)

Or 1 J = 1 W X 1 s

Thus, energy in joule is obtained if we multiply power (in watt) by time (in second). Alternatively, power can be in kilowatt (kW) and time can be in hour (h). In this way, kilowatt (kW) X hour (h) also represent energy unit.

We know that

1 kW = 1000 watt

And 1 hour (h) = 3600 seconds

Thus, 1 kW X h = 1000 W X 3600 s = 3,600,000 Ws

From Eq. (2.1), we know that 1 Ws = 1 J

Therefore, 1 kWh = 3,600,000 Ws = 3,600,000 J = 3,600 kJ

Or, using prefix kilo for 1000, we can write as follows :

1 kWh = 3,600,000 J = 3,600 kJ

In this way, energy unit ‘J’ can be converted into kWh or vice versa. Both of these units are commonly used to represent electrical energy as well as solar radiation energy. These units and their conversion from one unit to other units are important and one should understand these units carefully and thoroughly.

The commonly used electrical energy units and their conversion for each other are presented in Table 2.3.

**Table 2.3** Energy units and Their Conversion

Energy Unit | Equivalent Energy unit |

1 Joule | = 1 Ws (watt-second) |

1 Wh | = 3,600 Ws |

= 3,600 J | |

1 kWh (kilowatt-hour) | = 3,600 kJ |

= 3,600,000 J | |

1 kilo Joule (kJ) | = 1,000 J |

1 Mega Joule (MJ) | = 1,000,000 J |

1 Mega Joule (MJ) | = 278 kWh |

1 Giga Joule (GJ) | = 1000 MJ |

**EXAMPLE 2.1** A 200-watt fan runs for 12 hours every day. How much electrical energy it consumes in one day ? Give your answer in kWh.

** Solution** It is given that the power of the fan = 200 watt

The number of hours of usage per day = 12 hour

Now, electrical energy can be obtained by multiplying watt by hours.

Therefore, Electrical energy = watt X hours = 200 X 12 = 2400 watt-hour or Wh and therefore, we should divide the answer by 1000 as the value of prefix ‘kilo’ is 1000.

Hence, electrical energy consumed = 2400/1000 = 2.4 kWh.

Thus, the answer is 2.4 kWh.

**EXAMPLE 2.2 ** A household in Mumbai received the monthly electricity bill of 130 units (or 130 kWh). Calculate the electricity bill in terms of joules.

** Solution** Monthly bill of household is 130 units = 130 kWh

From Table 2.3, we can use the conversion between kWh and joules as follows :

1 kWh = 3,600,000 J

Therefore, 1300 kWh = 130 X 3,600,000 J = 468,000,000 J

**WORKSHEET 2.1 :** Fill the following table (Table 2.4) on energy units and their conversion from one unit to other unit :

** ****Table 2.4** Energy Units and Their Conversion

1 MJ | = …………………..kJ |

10 kWh | = …………………..J |

1000 J | = ………………… kWh |

1 kWh | = …………………Wh |

……………kWh | = 10,000 kJ |

1 MWh | = …………………kWh |

……………kJ | = …………………MJ |

……………kWh | = 5000 Wh |

10 kWh | = ……………….. units of electricity |

** **

**WORKSHEET 2.2 :** Fill Table 2.5 on estimation of electrical energy consumed by electrical appliances.

**Table 2.5** Estimation of Electrical Energy Consumed

Type of appliance | Power of the appliance | Daily duration of usage of appliance | Electrical energy consumed |

Tube light | 40W | 4 hours | = ..…..Wh |

Tube light | 40W | ….hours | = 400 Wh |

Fan 1 | 60W | 12 hours | = ..…..Wh |

Fan 2 | 30W | 12 hours | = ..…..kWh |

TV | 150W | 2 hours | = ..…..Wh |

Cooler | 200W | 10 hours | = ..…..kWh |

Computer | ……W | 2 hours | = 400 Wh |

LED Light | ……W | ….hours | = 20 Wh |

AC | 1.5 kW | 10 hours | = ..…..kWh |

AC | 1.5 kW | ……hours | = 7.5 kWh |

Unknown appliance | …..W | 10 hours | = 500 Wh |

Unknown appliance | …..W | 5 hours | = 10 kWh |

When we multiply the wattage of appliances with hours of usage in a day, we get energy used by appliance in a day.

**2.1.6 Power and Its Units**

Power is not same as energy. Many times, there are misconceptions and people tend to believe that energy and power are same and they use these two different terms for same meaning. One good place to identify the difference between these two terms is our own house. We pay electricity bill for the energy that we have consumed during the month. But when we talk about our appliances in terms of power; 10 watt bulb, 50-watt bulb, 1000 watt water heater, etc.

Power is the rate at which energy is used. The unit of power is watt and it is abbreviated as ‘W’. When one joule of energy is consumed in one second, it is referred as one watt of power consumption. The definition of the power can be presented in terms of the following equation :

Let us take an example of two CFL’s ; a 20-watt CFL and a 10-watt CFL. Since the power consumption of a 20-watt CFL consumes energy twice as fast as a 10-watt CFL. Thus, if both CFL’s are used for 1 hour, a 20-watt CFL will consume double energy ( 20 watt x 1 hour = 20 watt-hour) as compared to energy consumed by a 10 watt CFL (10 watt X 1 hour = 10 watt-hour). In this way, when we multiply watt (power unit) by hour (time unit), we get energy unit or when we divide energy unit by time we get power unit.

In practice, power plants capacities are mentioned in terms of MW (Megawatt = 106 watt) and the energy contents of the fuels like petrol, diesel, coal, etc. are mentioned in terms of MJ or kWh). The electricity bill is made in terms of kWh and the ratings of our appliances are given in terms of watt.

**Table 2.6 **Different Power Units and Their Equivalent Units

Power unit | Equivalent unit |

1 watt | = 1 joule – second = 1 W |

1 kilowatt (kW) | = 1000 watt or 1000 W |

1 megawatt (MW) | = 1,000,000 W |

1 Gigawatt (GW) | = 1,000,000,000 W |

**EXAMPLE 2.3** A tube light consumes 320 watt-hours of electrical energy when used for 8 hours. Estimate the power rating of the tube light.

** Solution** Given, energy consumption of tube light = 320 watt-hour

Time duration of usage of tube light = 8 hours

**WORKSHEET 2.3 :** Fill the following table (Table 2.7) on power units and their conversion from one unit to other unit.

**Table 2.7 **Power Units and Their Conversion

1 kW = ……. W |

1 MW = ……. kW |

2.4 kW = …….W |

200 W = ……. kW |

0.5 kW = …… W |

….. kW = 5000 W |

…… W = 0.3 kW |