Energy Transfers and the Principle of Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed. It can only be transferred from one store to another or transformed from one form to another. The total energy of a closed system remains constant.

Applying conservation of energy

In any energy transfer:

$\text{total energy input} = \text{useful energy output} + \text{wasted energy}$

The wasted energy is usually transferred to the thermal energy store of the surroundings by friction, air resistance, or electrical resistance. This energy is described as dissipated because it spreads out and becomes difficult to use.

Example: a light bulb

Electrical energy is transferred to light energy (useful) and thermal energy (wasted). The total energy output equals the electrical energy input.

Example: a roller coaster

At the top: maximum gravitational potential energy, minimum kinetic energy. At the bottom: minimum gravitational potential energy, maximum kinetic energy.

If no friction: the total mechanical energy (kinetic + gravitational potential) stays constant. In practice, some energy is transferred to thermal energy by friction with the track and air resistance, so the car does not return to exactly the same height.

Common errors and how to correct them

Saying energy is “used up.” Energy is conserved. The useful energy has been transferred to the surroundings as thermal energy, not destroyed.

Ignoring wasted energy in calculations. If a question gives both useful output and wasted output, check that they add up to the input. If they do not, there is a calculation error.

How to apply this in an exam

Always account for all energy. State where the useful energy goes and where the wasted energy goes. Use “transferred to the thermal energy store of the surroundings” rather than “lost as heat.”