How much?

So far we have introduced an energy perspective, seeing processes as shifting energy between different kinds of stores and along various pathways. Now we turn our attention to the question of how much energy is being shifted. Being able to answer this question is of great practical importance, whether in designing car engines, estimating the energy demands of a city or thinking about the insulating properties of a new material.

Calculating energy changes is not required of pupils in the 11–14 age range, although it certainly is during the next stage of schooling. We are therefore including much of the material in this episode to allow you, the teacher, to develop a broader and deeper understanding of the topic.

Thinking about lifting things is a good place to start investigating the how much? question. For example, how much energy is shifted when you lift a stool up onto the bench at school? How does this compare with the energy shifted when you lift a book up onto a shelf?

In both cases energy is shifted from the chemical store of your muscles to the gravitational store of the stool or book in the Earth's field. Furthermore, thinking back to the ideas of episode 03, the energy is shifted along a mechanical working pathway.

Lifting boxes

The amount of energy shifted in lifting the book or stool depends on just two things:

• The lifting force
• The height through which the object is lifted

In fact, you can calculate how much energy (in joules) is shifted by multiplying the force (in newtons) by the height (in metres).

Suppose the stool has a mass of 3 kilogram and the bench top is 1.5 metre above the floor. The energy shifted can be calculated energy = force of gravity × height (or, in symbols: E = F × d).

Working with this data:

energy = 30 N × 1.5 m

You can work out that the energy shifted is 45 J

Notice that here we are assuming that a 30 newton force is being used to lift the 3 kg mass. In other words, the lifting force is taken to be equal to the gravity force acting on the object. Underlying this assumption is the idea that the stool is lifted at a steady speed. Thus, once the stool is set into upwards motion, the lifting force equals the gravity force, the resultant force is zero and the stool moves at a steady speed. If this is not too clear you'll find more help in episode 02 of the SPT: Motion topic.

Dragging boxes

There are countless situations in which energy is shifted by mechanical working. For example, if I push my car along the road, energy is shifted from the chemical store of my muscles to the kinetic store of the car through mechanical working. All such cases involve a force acting for a certain distance (I might push my car 20 metre along the road) and the energy shifted can be calculated as follows:

energy = force × distance

With units:

energy/joule = force/newton × distance/metre

and, as symbols:

E = F × d

Here we are assuming that the force acting is constant in strength and direction throughout the movement and is along the same line as the distance moved. In general terms, the constant force exerted multiplied by the distance moved by the force (in the direction in which it is exerted) gives you the energy shifted from one store to another. Back to dragging boxes for a recap.

Other pathways

These calculations are further ahead in the pupils' learning, and are presented for completeness.

The energy shifted by electrical working can also be calculated and that has an episode all to itself (SPT: Electric circuits topic). Put briefly, energy is shifted through electrical working when charge passes through a voltage. For example, energy is shifted to the thermal store of the surroundings when charge passes through the resistive filament wire of a bulb, and we can measure the voltage drop with a voltmeter connected across the bulb.

Hot things can shift energy to another internal store in two different ways; by radiation and by particles. In neither case is it particularly easy to calculate the amount of energy shifted at this early stage, but by way of compensation the mechanisms for these two pathways are looked at in detail in episode 05. More on how to do the calculations is in the SPT: Electricity and energy topic.

energy shifted = charge passing × voltage drop

Or, with units:

energy shiftedjoule = charge passingcoulomb × voltage dropvolt

Energy, power and time

The amount of energy that is shifted to or from a store during one second is called the power. The unit of power is the watt (W).

Suppose a light bulb has a power of 100 watt. As a consequence, when the bulb is operating under normal conditions, it shifts 100 joule of energy each second from the chemical store of the supply to the internal store of the surroundings (along heating and lighting pathways).

If you know the power output for a device such as an electric bulb, you can calculate the energy shifted in a given time as follows:

energy = power × duration

energyjoule = powerwatt × durationsecond

And, expressed using symbols:

E = P × t

Shifting at different rates

Here is an example where energy is shifted to a kinetic store by accelerating a pellet.

There is a trade-off. You can have a big power for a short time, or a smaller power for a longer time. In both cases the same mass achieves the same top speed, and the same amount of energy is shifted into the kinetic store.

Energy shifting: tracking power

One way of starting to chart the quantity of energy shifting per second, the power, is to use a Sankey diagram. This kind of diagram is often used by power engineers and those concerned with power supply and demand. Sankey diagrams built of stylised arrows, where the thickness of arrow shows the the power in a particular pathway.

To represent the conservation of energy correctly the total thickness of the arrows must be constant.

Here, we'll estimate (rather than precisely calculate) the quantities of power, so supporting the semi-quantitative approach suitable for 11-14 pupils.

Drawing these diagrams provides an excellent starting point for thinking about power in a process, quantifying the pathways description.

Sankey diagrams are diagrams of processes in action, so complement the descriptions developed in terms of energy, which is always from snapshot to snapshot, so looking at the start and end points of a process.

Three examples

A coal fired power station connected to a domestic cooker.

There's not enough information to decide on the precise relative thickness of the arrows, so these diagrams are really plausible illustrative sketches.

Another pair of diagrams show how you can deal with an increased rate of dissipation, for a commonly used example.

Two cars at different speeds.

A car accelerating on the level.

You can chose to develop either power or energy descriptions: to describe the changes from snapshot to snapshot, or to describe the process happening, as here.

Power is about what's happening; energy is about what has happened or might happen

Simple calculations can find the energy shifted to or from a store between one time and another (from snapshot to snapshot). So these quantities are about complete processes: either analysing a process that has occurred, or about determining whether a potential process can or cannot happen. A natural way to represent these accumulations (whether positive or negative) is in terms of a bar.

The power in a pathway is a measure for a process that is incomplete: it is still happening when the measure is valid. A natural way to represent these accumulations (whether positive or negative) is in terms of a Sankey arrow, as these are essentially about flow.