Energy stores, transfers and conservation

An object can have more than one store at once. A moving, raised object has both kinetic and gravitational potential energy. For the same object in the same state, a higher temperature means more energy in its thermal store; temperature alone does not let us compare the total thermal energy of different objects.

Changes involve transfers between stores

When a system changes, energy is transferred. A falling apple gains speed: energy in the gravitational potential store of the apple–Earth system decreases while energy in the apple’s kinetic store increases. If air resistance is negligible, almost all of the decrease in gravitational potential energy becomes an increase in kinetic energy.

The store tells us where energy is held. The transfer pathway tells us how energy moves between stores:

• Mechanical working: a force transfers energy when it moves an object or changes its shape. Lifting an object increases its gravitational potential energy; stretching a spring increases its elastic potential energy.
• Electrical working: moving charges transfer energy in electrical equipment. In a kettle, energy is transferred electrically from the mains supply to the thermal store of the heating element.
• Heating: energy transfers from a hotter object to a colder one. The kettle’s hot element transfers energy by heating to the water.
• Radiation: waves carry energy between objects. Light from a lamp transfers energy to objects that absorb it.

These pathways are processes, not stores. For example, an electric kettle does not contain an ‘electrical energy store’: electrical working increases the thermal energy of its element.

Drawing and reading energy flow diagrams

An energy flow diagram uses boxes to identify stores and labelled arrows to identify transfer pathways. To construct one, identify the starting store or energy supply, the stores that increase, and how energy reaches them. Include unwanted transfers as well as the intended one.

For a kettle, electrical working heats the element. The element then heats the water, which is the intended result. However, the casing and surrounding air also become warmer.

Read the diagram by following each arrow from its starting point to its destination. The arrow label explains the process; the box label identifies where the energy is stored. This lets you distinguish the useful increase in the water’s thermal store from unwanted increases in other thermal stores.

Conservation keeps the energy account balanced

Conservation of energy means that energy cannot be created or destroyed. It can only be transferred between stores. In a closed system, transfers produce no net change in the system’s total energy:

$$E_{\text{total before}} = E_{\text{total after}}$$

Individual stores can still change. As an apple falls, its kinetic energy increases while gravitational potential energy decreases. Conservation does not mean that every store stays constant.

The system boundary matters. A hot mug loses energy as it warms the surrounding air. If we study only the mug, its thermal energy decreases. If we include the mug and everything receiving that energy, the decrease is balanced by increases elsewhere. Energy leaving one object has not disappeared.

Dissipation makes energy less useful

In real system changes, some energy is inevitably dissipated: it spreads out into less useful stores, usually thermal stores of the surroundings. The energy still exists, but it becomes difficult to collect and use for the original purpose.

Friction and air resistance cause this during movement. When a bicycle’s chain and gears rub together, energy is transferred mechanically into their thermal stores. They warm up and then transfer energy by heating to the surroundings. Not all the rider’s energy transfer therefore contributes to moving the bicycle.

Electrical equipment also warms up. In a kettle, increasing the water’s thermal energy is useful, but warming the casing and room is generally unwanted. In a filament lamp, the hot filament emits useful visible light, but much of the energy warms the surroundings instead.

‘Useful’ and ‘wasted’ describe whether a transfer helps achieve the intended task. Neither term changes the conservation rule: useful energy and wasted energy must both be included in the energy account.

Sankey diagrams show the amounts transferred

A Sankey diagram represents energy transfers using arrows whose widths are proportional to the amounts of energy. The input arrow splits into outputs: the useful output usually continues straight ahead, while wasted outputs branch away.

To draw one, choose a scale for the widths, draw the input arrow, and split it into output arrows using the same scale. The output widths must add up to the input width because energy is conserved:

$$E_{\text{input}} = E_{\text{useful}} + E_{\text{wasted}}$$

The following kettle diagram represents an electrical input of 1000 J. Of this, 800 J increases the water’s thermal energy and 200 J increases the thermal energy of the casing and surroundings.

Electrical energy input: 1000 J. Increase in water’s thermal energy: 800 J. Warming of casing and surroundings: 200 J. Wasted energy = 1000 − 800 = 200 J. Efficiency = 800 ÷ 1000 × 100% = 80%. Arrow shaft widths are proportional to energy.

The useful arrow is four times as wide as the wasted arrow because 800 J is four times 200 J. The two output amounts total 1000 J, matching the input. If the input and useful output are known, the wasted transfer is found by subtracting the useful output from the input.

$$E_{\text{total before}} = E_{\text{total after}}$$

Dissipation

Real system changes spread some energy into less useful stores, usually thermal stores of the surroundings. Friction, air resistance and electrical resistance cause unwanted warming. Wasted energy is not destroyed.

Transfer diagrams

Flow diagram: boxes identify stores; arrows identify pathways.

Sankey diagram: arrow widths show energy amounts. Output widths add up to the input width.

$$E_{\text{input}} = E_{\text{useful}} + E_{\text{wasted}}$$