Efficiency Formula
The efficiency formula \eta = \frac{\text{useful output}}{\text{total input}} \times 100\% measures how much of the input energy is converted to useful work. Real machines are always less than 100% efficient because some energy is lost as heat or friction.
The Formula
When to use: What fraction of the energy you put in actually goes where you want it to go, rather than being wasted as heat.
Quick Example
Notation
What This Formula Means
The ratio of useful output energy (or power) to total input energy, expressed as a percentage — always less than 100% due to energy losses.
What fraction of the energy you put in actually goes where you want it to go, rather than being wasted as heat.
Formal View
Worked Examples
Example 1
easySolution
- 1 Use the efficiency formula: \eta = \frac{\text{useful output}}{\text{total input}} \times 100\%.
- 2 Substitute the given values: \eta = \frac{350}{500} \times 100\%.
- 3 \eta = 70\%
Answer
Example 2
mediumCommon Mistakes
- Getting an efficiency above 100% — this means you mixed up input and output or made a calculation error; efficiency cannot exceed 100% by conservation of energy.
- Confusing efficiency with power — a low-power device can be highly efficient, and a high-power device can be very inefficient.
- Forgetting to express efficiency as a percentage — dividing output by input gives a decimal (e.g., 0.25), which must be multiplied by 100 to get 25%.
Why This Formula Matters
Efficiency is central to engineering design, energy policy, and sustainability. It explains why LED bulbs use less electricity than incandescent bulbs for the same light, why electric motors are more efficient than combustion engines, and why power plants waste substantial energy as heat.
Frequently Asked Questions
What is the Efficiency formula?
The ratio of useful output energy (or power) to total input energy, expressed as a percentage — always less than 100% due to energy losses.
How do you use the Efficiency formula?
What fraction of the energy you put in actually goes where you want it to go, rather than being wasted as heat.
What do the symbols mean in the Efficiency formula?
\eta (eta) is the efficiency as a fraction or percentage, E_{\text{useful}} is useful output energy in joules, E_{\text{total}} is total input energy, T_H and T_C are the hot and cold reservoir temperatures in kelvin.
Why is the Efficiency formula important in Physics?
Efficiency is central to engineering design, energy policy, and sustainability. It explains why LED bulbs use less electricity than incandescent bulbs for the same light, why electric motors are more efficient than combustion engines, and why power plants waste substantial energy as heat.
What do students get wrong about Efficiency?
High efficiency doesn't mean low power use—it means less waste.
What should I learn before the Efficiency formula?
Before studying the Efficiency formula, you should understand: energy, work.