Dissipated Energy and Calculating Efficiency

Dissipated energy is energy that spreads into the surroundings as less useful thermal energy, and efficiency is the fraction of the total energy input that is transferred to a useful form: efficiency = useful energy output ÷ total energy input (× 100 for a percentage). In brief: no real machine is 100 percent efficient, because some energy is always dissipated by friction, electrical resistance, sound and heat. The same ratio can be used with power: efficiency = useful power output ÷ total power input.

A filament lamp wastes most of its electrical energy as heat, and a petrol engine converts less than half of the fuel’s energy to motion. Efficiency measures how well a device uses energy. This guide explains dissipation, gives the efficiency formula, shows how to improve efficiency, compares devices in a table, works through calculations and corrects common mistakes.

What is dissipated energy?

When energy is transferred, part of it usually goes into stores that are not useful for the purpose of the device: mainly the thermal energy of the surroundings, which is spread over many particles. This is called dissipation (wasted energy). Typical causes are friction between moving parts, electrical resistance in wires, air resistance and sound. Dissipated energy cannot easily be gathered and used again, but it is still part of the total, so the principle of conservation of energy holds: useful output + wasted output = total input.

How is efficiency calculated?

Efficiency = useful energy output ÷ total energy input

It is a number between 0 and 1, or a percentage between 0 and 100 percent. Equivalent forms: efficiency = useful power output ÷ total power input, and efficiency = 1 − (wasted energy ÷ total input). Efficiency above 100 percent would break the law of conservation of energy. (Heat pumps and refrigerators may have a coefficient of performance greater than 1, because they move thermal energy rather than create it, which is a different measure.) Sankey diagrams show the flow of energy, with the width of the arrows proportional to the energy.

How can efficiency be improved?

• Lubricate moving parts and use ball bearings to reduce friction.
• Streamline vehicles to reduce air resistance.
• Use thermal insulation in buildings, hot water tanks and kettles.
• Use thick copper wires for lower resistance, and LED lamps instead of filament lamps.
• Recover waste heat, for example in combined heat and power plants.

Typical efficiencies

Worked example: efficiency calculations

1. Motor. An electric motor takes in 800 J of electrical energy and lifts a load, gaining 600 J of gravitational potential energy. Efficiency = 600 ÷ 800 = 0.75 = 75 percent. Wasted energy = 800 − 600 = 200 J (thermal and sound).
2. Power form. A 60 W filament lamp is 5 percent efficient. Useful light power = 0.05 × 60 = 3.0 W. Wasted power = 57 W as thermal energy.
3. Comparing lamps. An LED that gives the same 3.0 W of light with an efficiency of 30 percent needs an input power of 3.0 ÷ 0.30 = 10 W. Over 1,000 hours, the filament lamp uses 60 kWh and the LED 10 kWh, a saving of 50 kWh.
4. Finding the input. A machine is 40 percent efficient and must deliver 2,000 J of useful work. Input = 2,000 ÷ 0.40 = 5,000 J, of which 3,000 J is wasted.

How did efficiency become important?

Sadi Carnot analyzed the efficiency of steam engines in 1824, and found the maximum possible value for a heat engine operating between two temperatures. James Watt improved the efficiency of steam engines in the 1760s by adding a separate condenser. In the twentieth century, concern about fuel costs and emissions led to energy labels on appliances and efficiency standards for cars and buildings.

Which mistakes are common?

Mistake 1: Saying that wasted energy disappears

It is transferred to the surroundings, mainly as thermal energy.

Mistake 2: Putting the total input on top of the fraction

Efficiency is useful output divided by total input, so it cannot exceed 100 percent.

Mistake 3: Mixing energy and power

Use both numerator and denominator in joules, or both in watts.

Mistake 4: Assuming that a more efficient machine is always more powerful

Efficiency and power are different quantities.