Energy and power

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I was talking to a friend recently – well-informed and technical, though not a physicist or engineer – who asked me if I could briefly clarify the subtle differences between ‘energy’ and ‘power’. ‘Subtle?! You mean you don't know?‘... is what I managed not to say. But why would they know? The ideas are ones that most folk need only a vague understanding of; and those who do have to care – the physicists and engineers – have the fundamentals drilled into them so early in their education, that they forget ever not knowing.

With energy bills in the news now, and renewable sources not yet in the news enough, it's probably useful to shed a little clarity here, and the distinctions are not, I think, as subtle as you may fear.

Power

Of the two ideas, I think power is the easier one to grasp:

Power is the rate at which something does work.

We'll come back to the words ‘rate’ and ‘work’ later, but the intuition you probably have, from that description, is accurate. A horse is more ‘powerful’ than a human, because it can pull a bigger load, or, with suitable ropes and pulleys, lift a weight faster; and a tractor is more powerful than both, because it can pull or lift more than either. The horse can deliver more power than the human, and we can put a number to that amount of power and call it (more or less) one ‘horsepower’.

Horsepower

James Watt standardised the notion of one horsepower, as a way of making his and Matthew Boulton's engines' output intelligible to buyers who were familiar with what horses could achieve. He settled on ‘one horsepower’ as the power required to raise 550 pounds at one foot per second (that's 10lb short of 40 stone), or, in modern terms, the power required to raise 76kg at one metre per second. Watt wasn't the first or last to try this measurement of working horses, and his number sits in the middle of quite a broad range of conclusions, but he and Boulton sold the most engines, and it's his definition that has stuck.

Some splendid ploughhorses

Some splendid ploughhorses

A fit human can produce about a tenth of a horsepower for an extended period – that is, if you were set to work for a shift, pulling on a rope, hauling up a 7.6kg weight at one metre per second, you'd be producing a tenth of a horsepower while doing it. A tractor can obviously produce substantially more, for a lot longer than one shift – cue agricultural revolution, and a change in horses' working lives.

A Watt-type beam engine

A Watt-type beam engine

Watt and Boulton's customers were interested in lifting water from mines, in bringing machinery up to speed, and in keeping machinery moving against friction. These are all nicely concrete examples of ‘mechanical work’, though even here some subtleties are clear: the raised water or the spinning machinery is clearly the outcome of work, but where does the work invested in the friction go to (we'll come back to this, too)?

The watt

The ‘horsepower’ is a usefully-sized unit if you're a 19th century mill-owner or farmer, but for everyone else, there's the watt. This is indeed named in honour of James Watt, and is measuring exactly the same thing as the horsepower, differing only in size, being defined in a way which is coherent with the other units of science and engineering. A watt is quite a small unit of power – a horsepower is about 750W – so we end up seeing the kilowatt, or a thousand watts, more often (there are several slightly different definitions of the horsepower: I'm going to stick with 750W here, as a nice round number). Thus a horsepower is about 0.75 kW.

Sizes

To get a feel for how big a watt is:

An offshore wind turbine

An offshore wind turbine

These are all different types of power: a power station might burn one or other type of fuel, or capture the wind, to create electrical power. A car might store that power in a battery, and then turn it into motion, or might do the same trick after carrying its own carbon-based fuel. A factory might use electrical or carbon-based power to make things, or dissipate it in noise, vibration and heat. But all of that effort can be described and quantified, one way or another, in watts.

So much for power.

Energy

What happens to power, when it's consumed? What's the effect of power consumption?

Above, I mentioned that

Power is the rate at which something does work.

The notion of power always implicitly contains a ‘per second’ within it – it's always a rate rather than an amount. That rate can be related to the amount of electricity going through a wire, or the amount of fuel going into an engine, but one way or another, it's ‘work being done’ or ‘work doing’. The end result of this accumulation is ‘work done’, or ‘energy’.

Energy is one of the foundational notions of physics and engineering, but when you look closely at it, it's a slippery thing to grasp, because it can take so many forms.

Work done

When a one horsepower horse raises 76kg at 1m/s, it's doing work, in both the informal sense of the word ‘work’, and the physicist's technical sense. After 100s, say, the weight is 100m higher than it was. If the horse laboured half as much, doing half a horsepower of work and so raising the weight at only 0.5m/s, but for twice as long, it would have produced the same effect: the weight is in the same place, the same total work has been done. A human working at 0.1 horsepower would have to work 10 times as long to raise the weight 100m, but again with the same end result.

That ‘sameness’ is the key thing, for the physicist: it doesn't matter how you got it there, the weight sitting 100m up in the air represents the same ‘work done’, no matter whether it got there slowly or quickly, hauled there by a human, a horse, a tractor, or a long-suffering ant with a miraculously friction-free block and tackle. You could attach the weight to a generator and let it generate electricity as it came back down again; or let it fall, apply brakes, and make the brake disks very hot; use it as a really big hammer; or do lots of other things which would take the energy stored in the raised mass, put there by the application of work, and turn it into energy of another sort, be it other mechanical energy, electrical energy, heat energy, noise, or something else.

Heat

Heat is one of those other forms of energy. When you pass electrical power through a heater – be it a fan heater or an electrical kettle – you are not storing up obviously reusable energy like you are when you raise a weight, but instead turning it into heat, which initially appears to be a very different kind of thing, and something which, until the mid-19th century was indeed regarded as a qualitatively different substance.

From the mid-18th to the mid-19th century, the flow of heat was mentally modelled as the flow of a substance, called ‘caloric’, which was neither created nor destroyed, and which was present in greater quantities in hot things than in cold things, physically moving from the cold to the hot as part of the process of ‘heating’. This was a broadly successful theory, and much of the thermodynamics of the 19th century was developed on the basis of this model. This 19th century thermodynamic theory is stil used and taught now, though starting from a slightly different place.

It is James Joule, a Salford brewer with a hard-headed interest in factory efficiency, who is credited with demonstrating that heat can be generated directly from mechanical work in a way incompatible with the caloric theory. That theory dropped from sight, and it, and the idea of the conservation of caloric, were replaced by the more general idea of the conservation of energy in whatever form it took, mechanical, thermal, electrical, chemical, gravitational, and indeed in any other process, natural or technological, governed by physical law.

Joule's heating apparatus

Joule's heating apparatus

This interconvertability may seem obvious to us now – of course friction makes things hot, electrical power makes a motor or my computer warm, and a steam engine can turn chemical fuel into heat and into motion – but getting the story straight, and discovering just how deeply the equivalence runs, involved exploring a lot of blind alleys. The discovery of the conservation of energy was one of the key breakthroughs of 19th century physics.

Measuring work done

One way of quantifying the amount of ‘work done’ is to ask ‘how much power, for how long?’ Whether our industrious horse works for 10s or the human works for 100s, they will have raised this same 76kg load the same amount. The horse has done 750W for 10s, which we can write as 750 times 10 or 7500 watt-seconds (‘watts by seconds’; note that this is emphatically not the same thing as ‘watts per second’). We write this as 7500Ws. The human instead applies 0.1 horsepower, or 75W for 100s, which is less ‘work being done’ but being done for longer and giving, again, 7500Ws. Thus the ‘watt-second’ is a measure of the end result of applying power – the ‘work done’, or ‘energy’.

The watt-second is, as with the watt above, quite a small amount of energy. You can accumulate a more substantial amount by absorbing 1kW of power for 1 hour, giving the familiar energy unit of the kilowatt-hour, the kWh.

If you run a 1kW heater for an hour, you have consumed 1kWh of electrical power, and turned it into 1kWh of heat energy in the room.

The watt-second is also known to physicists as the ‘joule’, with multiples kilojoule (kJ), megajoule (MJ) and so on, and it is indeed named after Mr Joule the brewer.

There are lots of other energy units. There's the volt-amp (VA) you might see on a battery to indicate its storage capacity, the ‘calorie’ traditionally used for the energy contained in food, the ‘ton of TNT’ for explosions, the ‘tonne of oil equivalent’, the ‘british thermal unit’ (a unit still in vogue in the USA, but which makes me think of cold radiators and tweed). They're all measuring the same thing – energy, or work done – but in units which are convenient in different contexts.

Costs, financial and environmental

What you pay for, in your utilities bill, is not power but energy. That's why your electricity bill is charged in pennies per kWh. Your gas meter reports usage in cubic metres of gas, but the gas supplier will keep records of the ‘calorific value’ of the gas they've supplied to you, which records how much energy is available per unit volume of the gas mixture they've actually piped to your house, in megajoules-per-cubic-metre: what you're paying them for is this calculated quantity of delivered energy, which will be a number in kWh.

An electricity meter

An electricity meter

Once you're familiar with the distinction between energy flow, measured in watts, and energy stored, measured in joules or kWh, you're starting to think like a physicist, analysing the world in terms of the movement and transformation of energy from one form and one place to another.

For example, a one tonne car moving at 100 km/hr has a kinetic energy – energy stored in that motion – which works out at 0.1kWh. If the driver applied the brakes to bring this car to a halt, that energy would be transferred to the brake disks, heating them with enough energy to bring 1.6kg of water to the boil in however many seconds it takes to stop the car; that energy is briefly stored in the brake disks before being transferred to, and briefly warming, the air around it (yes, that energy is discarded into hot air every single time the car comes to a halt, and is put back into the car by burning fuel). This kinetic energy is associated purely with the car's speed, and is put into the system by the engine when it accelerates the car. It is distinct from the power required to keep the car cruising at speed, which replaces the energy lost to rolling resistance (heating the tyres and making noise), mechanical resistance (in the engine and axles and, again, noise), and wind resistance.

A car with glowing brake disks

A car with glowing brake disks

If the car were an electric one rather than a fossil-fueled one, it would be using the same amount of energy to get up to and stay at speed, retrieving it from its storage place in the battery; it arrived in the battery after being transported from a power station; and it was generated at that power station by burning fuel, by converting the wind's kinetic energy to electrical energy, by wrangling electrons in a photovoltaic cell, by rearranging nuclei in a reactor, or by some other more exotic means.

Thinking of energy as a thing encourages you to mentally trace where that energy came from – it always came from somewhere – and how quickly it did so. Attaching numbers to these flows and stores, whether watts or kWh, also lets you answer the question ‘is that a lot or a little?’ That's a crucial question, because there is a precisely describable difference between the amount of energy consumed in leaving a light on, and in driving to the shops (one of these numbers is bigger than the other).

What you do with that information is of course Step Two.

Norman, 2022 #f 20