Energy Transfers and Conservation of Energy
The law of conservation of energy states that energy cannot be created or destroyed, only transferred from one store to another or converted from one form to another, so the total energy of an isolated system stays constant. In brief: energy transfers happen by work (forces), heating, electrical currents and waves. To solve problems, write the energy at the start and at the end: Einitial = Efinal + energy dissipated. Energy diagrams (Sankey diagrams) show these transfers.
When a ball is thrown, a kettle boils or a car brakes, energy changes form, but the total remains the same. This is one of the most useful principles in science. This guide states the law, shows the main transfers, explains how to use it in calculations, compares examples in a table, works through problems and corrects common mistakes.
What does the law say?
In a closed (isolated) system, the total energy is constant. If the system exchanges energy with its surroundings, then the change in the energy of the system equals the energy transferred in or out. In everyday situations, it can seem that energy is lost, for example when a bouncing ball stops: the kinetic energy has been transferred to thermal energy of the ball, floor and air, and some to sound. The energy is still there, but spread out and not useful.
What are the energy transfers?
- Mechanical work: a force moves an object through a distance, W = Fs.
- Heating: thermal energy moves from a hotter object to a colder one by conduction, convection or radiation.
- Electrical work: a current transfers energy through a circuit, E = VIt.
- Waves: light and sound transfer energy outward from the source.
Examples of energy conversion: in a hydroelectric power station, gravitational potential energy of water becomes kinetic energy, then electrical energy via turbines and generators; in a battery-powered torch, chemical energy becomes electrical, then light and thermal energy.
How is the law used to solve problems?
- Identify the system and the two moments (start and end).
- List all energy stores at the start and the end.
- Write the equation: total energy at start = total energy at end + energy transferred out (if any).
- Solve for the unknown, and check the unit (joules).
Examples of energy transfers
| Device | Energy input | Useful output | Wasted output |
|---|---|---|---|
| Electric motor | Electrical | Kinetic | Thermal, sound |
| Loudspeaker | Electrical | Sound | Thermal |
| Solar cell | Light | Electrical | Thermal |
| Car engine | Chemical | Kinetic | Thermal, sound |
| Bouncing ball | Gravitational potential | Kinetic, then potential | Thermal, sound |
Worked example: a pendulum and a roller coaster
- Pendulum. A bob is raised 0.20 m above its lowest point and released. Ignore friction. At the lowest point, all the gravitational potential energy is kinetic: mgh = ½mv2. The mass cancels, so v = √(2gh) = √(2 × 9.8 × 0.20) = √3.92 = 1.98 m/s, about 2.0 m/s.
- Roller coaster. A car (mass 500 kg) starts from rest at the top of a 10 m hill. Speed at the bottom, if friction is negligible: v = √(2 × 9.8 × 10) = √196 = 14 m/s.
- With losses. If 5,000 J of the energy is dissipated by friction, the initial energy is mgh = 500 × 9.8 × 10 = 49,000 J. The kinetic energy at the bottom is 49,000 − 5,000 = 44,000 J, so v = √(2 × 44,000 ÷ 500) = √176 = 13.3 m/s.
- Kettle. A 2.0 kW kettle runs for 3.0 min and transfers 360 kJ from the electricity. If 90 percent heats the water, the thermal energy gained is 324 kJ, and 36 kJ is lost to the surroundings.
How was the law established?
Julius Robert von Mayer (1842), James Joule (1843 to 1850) and Hermann von Helmholtz (1847) independently developed the principle of conservation of energy. Joule’s paddle-wheel experiment, in which falling weights stirred water and warmed it, measured the mechanical equivalent of heat. The law was later connected with symmetry in time by Emmy Noether (1918). Einstein’s relativity extended the law to include mass as a form of energy.
Which mistakes are common?
Mistake 1: Saying that energy is lost
It is dissipated to the surroundings and no longer useful, but it is not destroyed.
Mistake 2: Ignoring one of the stores
List all stores at the start and the end, including thermal energy if there is friction.
Mistake 3: Using mechanical energy conservation with friction
With friction, mechanical energy is not conserved, but total energy is.
Mistake 4: Forgetting that the mass cancels in free-fall problems
The speed from a fall depends on the height only, not the mass.