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# What are different Units of Energy?

## Units of Energy

The capability of an object to do work is called its energy. In electrical engineering, the most important forms of energy are electrical energy, mechanical energy and thermal energy. Different units of measurement are used for the various forms of energy. Although, the units of electrical, mechanical and thermal energies are interchangeable.

The units of various forms of energy are described as follows −

## Mechanical Energy

The mechanical energy is defined as the product of force and distance, i.e.,

$$\mathrm{\mathrm{Mechanical \:energy\:=\:Force\: in \:Newton\:\times \:distance\: in \:meters}}$$

Therefore, the SI unit of mechanical energy is **Newton-meter (Nm) or Joules (J).**

The mechanical energy of a body is equal to 1 N-m or J, if a force of 1 N moves the body through a distance of 1 meter.

$$\mathrm{\mathrm{1 \:Newton\: meter\:=\:1 \:Joule}}$$

## Electrical Energy

The total amount of work done in an electric circuit is called electrical energy. Mathematically, the electrical energy is equal to the product of voltage across the circuit, current flowing through the circuit and the time for which the current flowed in the circuit, i.e.,

$$\mathrm{\mathrm{Electrical\: Energy\:=\:Voltage \:in\: volts\:\times \:Current \:in \:amperes\:\times \:Time\: in \:seconds}}$$

$$\mathrm{\Rightarrow \mathrm{Electrical\: Energy\:=\:Power\: in \:watts\:\times \:Time\: in\: seconds}}$$

Where,

$$\mathrm{\mathrm{Power\: in\: watts\:=\:Voltage \:in\: volts\:\times\: Current\: in\: amperes}}$$

Therefore, the SI unit of electrical energy is **watt-sec (Ws)** or **Joule (J)**.

The electrical energy transferred between two points is equal to 1 Watt-sec or Joule, if a potential difference of 1 Volt exists between them and a current of 1 Ampere passes between them for 1 second.

The Watt-second or Joule is a very small unit of electrical energy. For practical purposes, the unit used for the measurement of electrical energy is **Watt-hour (Wh)** or **kiloWatt-hour (kWh).**

$$\mathrm{\mathrm{1\: Watt\: hour\:=\:1\: Watt\:\times \:1\: hour\:=\:1\: Watt\:\times \:3600\: sec\:=\:3600\: Watt\: sec}}$$

And,

$$\mathrm{\mathrm{1\: kiloWatt\: hour\:=\:1 kW\times\: 1\: h\:=\:1000 \:W\:\times\: 3600\: sec\:=\:36\:\times \:10^{\mathrm{5}} \:Watt\: sec}}$$

## Heat Energy

The form of energy which produces the sensation of warmth is known as heat energy. The SI unit of heat is **Joule (J)**. The other units of heat are **calorie**, **B.Th.U.** and **C.H.U.** which are defined as −

**Calorie**- One calorie is the amount of heat required to increase the temperature of 1 gm of water through 1 °C, i.e.,

$$\mathrm{\mathrm{1\: Calorie\:=\:1\: gm \:of \:water\:\times 1^{\circ} C}}$$

**B.Th.U.**- B.Th.U. stands for*British Thermal Unit*. It is the amount of heat required to increase the temperature of 1 lb of water through 1 °F, i.e.,

$$\mathrm{\mathrm{1\: B.Th.U.\:=\:1\: lb\:\times\: 1^{\circ}F}}$$

**C.H.U.**- C.H.U. stands for*Centigrade Heat Unit*. It is the amount of heat required to raise the temperature of 1 lb of water through 1 °C, i.e.,

$$\mathrm{\mathrm{1\: C.H.U.\:=\:1\: lb\:\times\: 1^{\circ}C}}$$

## Relationship among Various Units of Energy

The relationship between the units of electrical energy, mechanical energy and heat energy is described below −

**Relationship between Units of Electrical and Mechanical Energies**−$$\mathrm{\mathrm{1 \:kWh\:=\:1\: kW\:\times\: 1\: h\:=\:1000 \:W\:\times\:3600\: sec}}$$

$$\mathrm{\therefore \mathrm{1\: kWh\:=\:36\:\times\: 10^{5} \:Joules}}$$

It shows that the electrical energy can also be expressed in Joules.

**Relationship between Units of Mechanical and Heat Energies**−Relation between calorie and Joules is,

$$\mathrm{\mathrm{1\: calorie\:=\:4.18 \:Joules}}$$

Relation between C.H.U. and Joules is,

$$\mathrm{\mathrm{1\: C.H.U.\:=\:1\: lb\:\times\: 1^{\circ}C\:=\:453.6 gm\:\times \:1^{\circ}C\:=\:453.6\: calories}}$$

$$\mathrm{\Rightarrow \mathrm{1\: C.H.U.\:=\:453.6\:\times \:4.18 \:Joules\:=\:1896\: Joules}}$$

$$\mathrm{\therefore \mathrm{1\: C.H.U.\:=\:1896\: Joules}}$$

Relation between B.Th.U. and Joules is,

$$\mathrm{\mathrm{1\: B.Th.U.\:=\:1 \:lb\:\times\: 1^{\circ}F\:=\:453.6 gm\:\times\:\left(\frac{5}{9} \right )^{\circ}C\:=\:252\: calories}}$$

$$\mathrm{\Rightarrow \mathrm{1 \:B.Th.U.\:=\:252\:\times \:4.18 \:Joules\:=\:1053\: Joules}}$$

$$\mathrm{\therefore \mathrm{1\: B.Th.U.\:=\:1053 \:Joules}}$$

**Relationship between Units of Heat and Electrical Energies**−Relation between kWh and calories is,

$$\mathrm{\because \mathrm{1 \:kWh\:=\:36\:\times\: 10^{5}\: Joules\: and \:1\: calorie\:=\:4.18\: Joules}}$$

$$\mathrm{\Rightarrow \mathrm{1\:kWh\:=\:\frac{36\:\times 10^{5}}{4.18}\:calories\:=\:860\:\times \:10^{3}\:calories}}$$

$$\mathrm{\therefore \mathrm{1\: kWh\:=\:860\:\times \:10^{3}\: calories}}$$

Relation between kWh and C.H.U. is,

$$\mathrm{\because \mathrm{1 \:kWh\:=\:36\:\times\: 10^{5}\: Joules\: and \:1\:C.H.U. \:=\:1896\: Joules}}$$

$$\mathrm{\Rightarrow \mathrm{1\:kWh\:=\:\frac{36\:\times 10^{5}}{1896}\:C.H.U.\:=\:1898\: C.H.U.}}$$

$$\mathrm{\therefore \mathrm{1\: kWh\:=\:1898\: C.H.U.}}$$

Relation between kWh and B.Th.U. is,

$$\mathrm{\because \mathrm{1 \:kWh\:=\:36\:\times\: 10^{5}\: Joules\: and \:1\:B.Th.U. \:=\:1053\: Joules}}$$

$$\mathrm{\Rightarrow \mathrm{1\:kWh\:=\:\frac{36\:\times 10^{5}}{1053}\:B.Th.U.\:=\:3418\: B.Th.U.}}$$

$$\mathrm{\therefore \mathrm{1\: kWh\:=\:3418 \:B.Th.U.}}$$

Hence, the above discussion shows that the electrical, mechanical and thermal energy units are interchangeable.

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