Energy stores, transfers and conservation

For example, a kettle receives energy electrically. This increases the energy in the heating element's thermal store. Energy then transfers by heating from the hot element to the water.

Choosing a system and conserving energy

A system is an object or group of objects chosen for study. You might study just a falling ball, or the ball together with Earth and the surrounding air. Choosing the system helps you decide which transfers to include.

Conservation of energy means that energy cannot be created or destroyed: it can only be transferred between stores. In a closed system, energy transfers cause no net change in the total energy. Individual stores can increase or decrease while their total remains constant.

For a falling ball, the gravitational potential store decreases as the kinetic store increases. If air resistance is negligible, the decrease in gravitational potential energy equals the increase in kinetic energy. With air resistance, some energy also transfers to thermal stores of the ball and surroundings. The ball gains less kinetic energy, but energy has not disappeared.

The boundary matters. A kettle and its water receive energy from outside through the mains supply, so their total stored energy increases while the kettle heats. This does not contradict conservation of energy: the energy has been transferred into the chosen system.

Calculating changes in gravitational potential energy

Lifting an object transfers energy to its gravitational potential store. The increase depends on its mass, the gravitational field strength and the vertical height gained:

$$\Delta GPE = m \times g \times \Delta h$$

Here, $\Delta GPE$ is the change in gravitational potential energy in joules (J), $m$ is mass in kilograms (kg), $g$ is gravitational field strength in newtons per kilogram (N/kg), and $\Delta h$ is the change in vertical height in metres (m). The symbol $\Delta$, pronounced ‘delta’, means ‘change in’.

Gravitational field strength describes the gravitational force on each kilogram of mass. Near Earth it is approximately 10 N/kg. Raising a greater mass, raising it higher or raising it in a stronger gravitational field requires a greater transfer of energy.

For example, a 4 kg box is lifted through a vertical height of 1.5 m where $g = 10\text{ N/kg}$:

$$\Delta GPE = 4 \times 10 \times 1.5 = 60\text{ J}$$

The box's gravitational potential store increases by 60 J. Lowering it through the same height decreases that store by 60 J. The height change is vertical: carrying it up a long slope to the same height gives the same increase in gravitational potential energy.

Calculating kinetic energy

Kinetic energy is the energy associated with motion. It depends on mass and speed:

$$KE = \frac{1}{2} \times m \times v^2$$

$KE$ is measured in joules (J), $m$ in kilograms (kg), and speed $v$ in metres per second (m/s).

For example, a 2 kg trolley moving at 3 m/s has:

$$KE = \frac{1}{2} \times 2 \times 3^2 = 9\text{ J}$$

This is the energy in its kinetic store. At the same speed, doubling the mass doubles the kinetic energy. Speed has a larger effect because it is squared: doubling the speed gives four times the kinetic energy.

Following energy through changing systems

An object projected upwards or up a slope: during the launch, energy transfers mechanically from the thrower's chemical store to the object's kinetic store. As the object rises, its kinetic store decreases and its gravitational potential store increases. It slows down as it gains height. Ignoring air resistance or friction, the kinetic energy lost equals the gravitational potential energy gained. At the highest point of a straight vertical throw, the object's speed is momentarily zero.

A moving object hitting an obstacle: the object's speed falls rapidly, so its kinetic store decreases. Forces during the collision transfer energy mechanically, causing deformation and increasing thermal stores of the object, obstacle and surroundings. Sound also carries some energy away. The kinetic energy has been transferred, not destroyed.

An object accelerated by a constant force: a resultant force acting in the direction of motion transfers energy mechanically to the object's kinetic store. Its speed and kinetic energy increase. For example, a person pushing a trolley transfers energy from their chemical store to the trolley's kinetic store. A constant force does not mean a constant speed.

A vehicle slowing down: the vehicle's kinetic store decreases. Friction during braking transfers energy to thermal stores of the brakes, tyres, road and surroundings. The brakes warm up as the vehicle loses speed.

Water brought to the boil in an electric kettle: energy transfers electrically from the mains supply to the heating element's thermal store, then by heating to the water's thermal store. The water's temperature rises towards boiling. Some energy also transfers to the kettle and surrounding air.

Drawing and reading energy flow diagrams

A flow diagram represents stores with labelled boxes and transfers with labelled arrows. To draw one, identify the store that decreases, the store that increases and the pathway connecting them. Add branches if energy transfers to more than one destination.

Read this diagram from left to right. ‘Electrically’ and ‘by heating’ label pathways, whereas the boxes identify thermal stores. The branch to the surroundings shows why not all the energy supplied ends up in the water.

Showing amounts with a Sankey diagram

A Sankey diagram shows the amounts transferred as well as their destinations. Arrow widths are proportional to energy: a wider arrow represents a larger transfer. The input arrow must be as wide as the output arrows combined.

Energy supplied electrically: 200 J. Increase in load's gravitational potential energy: 150 J. Energy transferred to thermal stores: 50 J. Wasted energy = 200 − 150 = 50 J. Efficiency = 150 ÷ 200 × 100% = 75%. Arrow shaft widths are proportional to energy.

In this motor example, 200 J is supplied electrically and 150 J increases the raised load's gravitational potential store. The remaining $200 - 150 = 50\text{ J}$ transfers to thermal stores. This is called wasted energy because it does not perform the intended job of lifting the load, not because it has been destroyed.

To draw this Sankey diagram, you could use 1 mm of arrow width for every 10 J: the input would be 20 mm wide, and the outputs 15 mm and 5 mm wide. To interpret any Sankey diagram, check that all output amounts add up to the input:

$$\text{Total energy supplied} = \text{Useful energy transferred} + \text{Wasted energy transferred}$$

• Energy cannot be created or destroyed, only transferred between stores.
• In a closed system, total energy remains constant even when individual stores change.
• Flow diagrams: boxes show stores; labelled arrows show pathways.
• Sankey diagrams: arrow width represents energy; input equals all outputs combined.

Changes to recall

• Projected upwards or up a slope: kinetic store decreases; gravitational potential store increases.
• Hits an obstacle: kinetic store decreases; deformation, thermal transfers and sound result.
• Accelerated by a constant resultant force: mechanical transfer increases the kinetic store.
• Vehicle slows: kinetic store decreases; thermal stores of brakes and surroundings increase.
• Kettle boils water: electrical transfer to the element, then heating to the water.

Ignoring resistance, gravitational potential energy gained equals kinetic energy lost during upward motion.