Class 9 > Unit # 08:Energy Sources & Transfer of Energy > Efficiency & Power

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Efficiency and Power: Definitions, Formulas, and Units

Q.6 Define and describe Efficiency.

Efficiency

"The ratio of output to the input is called efficiency."

Description

Every machine needs some energy to perform work. Whatever energy is given to a machine is called input ($E_1$), and the useful work done by the machine is called output ($E_2$).

Efficiency is denoted by the Greek letter eta ($\eta$). Mathematically, it is expressed as:

$\text{Efficiency } (\eta) = \frac{\text{Output}}{\text{Input}} = \frac{E_2}{E_1}$

$\text{Percentage Efficiency } (\eta \%) = \left(\frac{\text{Output}}{\text{Input}}\right) \times 100\%$

Fig: Energy flow diagram of a practical machine showing input, useful output, and energy losses.

Unit

As efficiency is the ratio of two similar quantities (energies or powers), it has no unit and is often expressed as a percentage.

Note

"No machine is 100% efficient because some energy is always wasted in the form of heat, sound, or light due to friction and air resistance."

Q.7 Define Power, its formula and unit.

Power

"The rate of doing work or the amount of energy transferred per unit time. Since work and time are scalar quantities, power is also a scalar quantity."

Formula

$P = \frac{W}{t}$

Where $W$ is the work done (or energy transferred) and $t$ is the time taken.

Since $W = F \cdot d$, power can also be written in terms of velocity ($v = \frac{d}{t}$):

$P = \frac{F \cdot d}{t} = F \cdot v$

Units of Power

In the SI system, the unit of power is the Watt (W), which is equivalent to joule per second ($\text{J/s}$).

$1 \text{ Watt} = \frac{1 \text{ Joule}}{1 \text{ Second}} \quad \Rightarrow \quad 1 \text{ W} = 1 \text{ J}\cdot\text{s}^{-1}$

Definition of 1 Watt: The power of a body is said to be one watt if it does work at the rate of one joule per second.

Other Units

• Kilowatt ($\text{kW}$): $1 \text{ kW} = 1000 \text{ W} = 10^3 \text{ W}$
• Megawatt ($\text{MW}$): $1 \text{ MW} = 1,000,000 \text{ W} = 10^6 \text{ W}$
• Horsepower ($\text{hp}$): $1 \text{ hp} = 746 \text{ W}$

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