Efficiency can be calculated using either energy values (Joules) or power values (Watts). The result is identical because power is simply energy per unit time.
Energy Formula:
Power Formula:
To express the result as a percentage, multiply the decimal value by 100:
Unitless: Since the numerator and denominator have the same units (J/J or W/W), they cancel out. Efficiency has no units.
Input vs. Output: Input is the energy supplied to the device (e.g., chemical energy in fuel). Output is the energy transferred by the device (e.g., kinetic energy of a vehicle).
Useful vs. Wasted: Useful energy corresponds to the intended function (e.g., light from a bulb). Wasted energy is the byproduct (e.g., heat from a bulb).
Decimal vs. Percentage: An efficiency of is exactly the same as . In calculations, always convert percentages to decimals (divide by 100) before using them in algebra.
Sanity Check: Efficiency can NEVER be greater than 1 (or 100%). If your calculation yields 1.2 or 120%, you have likely swapped the numerator and denominator.
Unit Consistency: Ensure both input and output are in the same units before dividing. You cannot divide Kilowatts (kW) by Watts (W) directly; convert one first.
Rearranging Formulas: Exams often give the efficiency and the input, asking for the useful output. Rearrange to:
Contextual Answers: When asked how to improve efficiency, do not just say "reduce waste." Specify the mechanism (e.g., "lubricate the gears to reduce friction" or "streamline the shape to reduce air resistance").
Conservation of Energy: Efficiency calculations are a direct application of the Law of Conservation of Energy. Total Input = Useful Output + Wasted Output.
Power: Since , efficiency problems often link to power calculations. You may need to calculate power first using work done and time before calculating efficiency.
Thermal Physics: Wasted energy usually ends up in the thermal store of the surroundings, linking efficiency to topics like specific heat capacity and thermal insulation.
