Define efficiency as: (a) (%) efficiency = (useful energy output) / (total energy input) (× 100%) (b) (%) efficiency = (useful power output) / (total power input) (× 100%) recall and use these equations

1.7.3 Energy Resources – Efficiency

Learning Objective

Define efficiency and use the following equations to calculate it:

1. Percentage efficiency based on energy:

   \$\text{Efficiency (\%)} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%\$

2. Percentage efficiency based on power:

   \$\text{Efficiency (\%)} = \frac{\text{useful power output}}{\text{total power input}} \times 100\%\$

What is Efficiency?

Efficiency measures how well a device or system converts the energy (or power) supplied to it into useful work or output. Because some energy is always lost as heat, sound, light, or other forms, the efficiency is always less than 100 %.

Key Points

• Efficiency is expressed as a percentage.
• It can be calculated using either energy or power; the result is the same because power is the rate of energy transfer.
• A higher efficiency means less waste and often lower operating costs.
• Typical efficiencies vary widely between different energy resources and technologies.

Using the Equations

When you know the useful output and the total input, substitute them directly into the appropriate formula.

Example (energy form):

\$\text{Efficiency (\%)} = \frac{2500\ \text{kJ (useful)}}{5000\ \text{kJ (input)}} \times 100\% = 50\%\$

Example (power form):

\$\text{Efficiency (\%)} = \frac{1.2\ \text{kW (useful)}}{2.0\ \text{kW (input)}} \times 100\% = 60\%\$

Typical Efficiencies of Common Energy Resources

Why Efficiency Matters

• Cost: Higher efficiency reduces fuel or electricity bills.
• Environment: Less waste energy usually means lower emissions.
• Design: Engineers aim to maximise efficiency within practical limits.

Sample Calculation – Coal Power Plant

Suppose a coal power plant receives 1.0 × 10⁹ J of chemical energy from coal and produces 3.2 × 10⁸ J of electrical energy.

\$\text{Efficiency (\%)} = \frac{3.2 \times 10^{8}\ \text{J}}{1.0 \times 10^{9}\ \text{J}} \times 100\% = 32\%\$

The remaining 68 % is lost as heat in the boiler, exhaust gases, and cooling system.

Practice Questions

1. A light bulb uses 60 W of electrical power and produces 12 W of visible light. Calculate its efficiency.
2. A hydroelectric dam releases water with a potential energy of 5.0 × 10⁹ J and generates 4.2 × 10⁹ J of electrical energy. What is its efficiency?
3. Compare the efficiencies of a gasoline car (25 %) and an electric car (90 %). If both travel 100 km, which uses less energy from the primary source? Explain briefly.

Key Take‑away

Efficiency provides a simple way to compare how well different energy resources and devices convert input energy into useful output. Mastery of the two efficiency formulas allows you to evaluate and optimise real‑world systems.