Lesson 2. What is energy?

In the quest towards low energy buildings, it's pretty important to have a good grasp of what energy is. My key questions for the lesson were: What is energy? How do you measure it? What is the second law of thermodynamics?

I should probably not have been surprised to find that some of my students didn't even know the first law of thermodynamics. So I told them a bit about James Joule, and the crucial link between beer and science that is often forgotten. The combination of the temperature-critical process of brewing, high-precision thermometers, newly developed electrical equipment and the desire to save money on the various industrial processes he was responsible for led Joule to discover and to prove that heat, work and energy were the same thing. Previously heat had been perceived as stuff. This was called caloric theory, and is where we get the unit of calories.

Calories are the normal measurement of energy in food, while we buy electrical energy in kilo watt hours, rate batteries in amp hours, buy oil in litres, gas in cubic metres or BTUs, and measure atomic energies in electron Volts. We're pretty confused about energy.

And as well as thinking of heat as stuff, and as the nights start to draw in, coming out with scientifically untenable concepts such as letting the cold in, we often intuitively confuse the idea of heat and temperature. To highlight this I asked two questions. First:

Which is hotter, a litre of hot air or a litre of hot water?

The answer is, of course, that they are the same. Actually, the question is, what do you mean hot? If we take hot as 80 degrees centigrade, then they are the same.

Next question:

Which has more heat, a litre of hot air or a litre of hot water?

Most people realise the answer is the hot water. Especially when it is rephrased: if you were to take a bottle to warm your bed, would you fill it with hot air or hot water?

Next question: How much hotter? 

I provided the specific heat capacity of Water (4.2 kJ/kgK) and the volumetric heat capacity of air (1.2 kJ/m³K) and they worked out that the bottle of water has over three thousand times more heat than the air.

And so to the first important teaching point: precision and accuracy. I showed them a picture of an analogue clock and a digital clock to demonstrate the difference. The analogue clock said it was five past eleven, when in fact it was twenty past. The digital watch said it was 14:27 and 36 seconds on the first of November. A much more precise answer, but several weeks less accurate.

People often confuse precision and accuracy, providing as many decimal places as possible and being fooled when many decimal places are provided. In all cases it is important to know the accuracy of the figures you put in, since the answer is going to be less accurate than these.

In the case of heat capacities, they change depending on the temperature, so the numbers are only accurate to within a few percent.

The other important thing is to know how accurate your answer needs to be.

In most cases, one significant figure is enough. You need to know whether the answer is 4 or 5. You don't need to know whether it is 4.13 or 4.12.

In the case of low energy buildings, we often need to choose between two alternatives and work out which will use less energy. A calculation to one significant figure will usually tell us. If we're choosing between water and air to transport heat through a pipe, we know that water will move over three thousand times more than air. It doesn't matter if it is three thousand or four thousand. In fact it doesn't matter whether it is three million or three.

And if the numbers are the same to one significant figure, then we may want to do a more accurate calculation. Or, more likely, we will decide that there is not much difference between the two alternatives in terms of energy use, and other factors may be more important, such as cost, or which one looks nicer.

So, it's important to know how accurate the numbers you use are, it's important to know how much accuracy you need, and you should not use more precision in your answers than your accuracy justifies.

After this digression from the meaning of energy, it was time for power.

Watt is the name of the inventor of the steam engine.

You have to say that with rising intonation for it to work properly.

He didn't actually invent the steam engine, but he probably invented global warming when he got one to work on a coal mine where it would pump water out of the mine, allowing them to dig out more coal, keep the pump pumping and so dig out even more.

He also gives his name to the unit of power. Power and energy is another source of confusion, with power the rate of change of energy. The use of kilowatt hours as a unit of energy does not help, although as a unit it's a pretty useful one.
One kilowatt hour is roughly equivalent to:
• leaving on a 100-watt lightbulb for 10 hours.
• 0.1 litres of paraffin　
• 0.1 m³ of gas
• 5 rice balls
• 20 litres of hot water
• 200 mobile phone batteries
• 0.04 milligrammes of uranium 235

(All figures are to one significant figure, except the atomic weight of uranium. Luckily I'm not teaching nuclear physics!)