The recent consultation on so-called “calories” on menus, together with the launch of more new models of electric cars has prompted these thoughts on the dysfunctional way in which we measure energy and power. This muddle reflects a lack of understanding of basic science and prevents people from making useful comparisons. We should standardise on the joule (J) and the watt (W).
Consider some of the different units that are or have been used for measuring energy and power (not an exhaustive list):
- British Thermal Units (BTU), typically for domestic boilers (although they usually mean BTU/h) – see below
- kilowatt hours (kWh), for electricity (and sometimes gas) bills
- joules (J) – the SI unit – used for food energy (nutrition) on package labels
- calories (cal) (often confused with kilocalories – kcal) also for food energy
- ergs – an obsolete unit from a previous version of the modern metric system
- electronvolts (eV) – used by physicists to measure very tiny quantities of energy
- horsepower (HP) – still sometimes used to describe car engine output
- brake horsepower (BHP) – now rarely used
- tax horsepower – formerly used to calculate tax on cars (e.g. Austin 7)
- Pferdestärke (PS) – a German version of HP for car engines
- chevaux fiscaux (CV) – similarly, a French version of “tax horsepower” (e.g. Citroën 2CV)
- watt – the SI unit, defined as a joule per second (J/s)
- British Thermal Units per hour (BTU/h) – used for heating systems
How – if at all – do all these units relate to each other? To explain this we need to revise a little basic science.
What are energy and power – and how do they relate?
There are various forms of energy (which may be why different measurement units have evolved), but they have one thing in common: energy is what makes things move, or heat, or light up, or make a sound. So it can be thermal (i.e. heat), or electro-magnetic, gravitational, or mechanical etc. But it is all energy. Energy cannot be created or destroyed, but one form of energy can be transformed into another form of energy – e.g. when a turbine generates electricity, which in turn heats a kettle or drives a motor: or when chemical energy stored in a battery is transformed into sound waves from your radio. As it is all basically the same “stuff” – energy – it is helpful if it can be measured in the same way.
Power is the rate at which energy is transformed – e.g. a 60 watt incandescent light bulb converts 60 joules of electrical energy every second into light and heat (mainly the latter by the way). Similarly, it is the rate at which chemical energy stored in petrol is transformed into mechanical energy to drive the car and generate electrical energy to charge its battery. Again, although it can take many forms, it is useful if it can be measured in the same way.
So if we were to measure energy and power using a single, common unit for each, which units should we choose, and what sort of comparisons would be possible?
For energy, the obvious choice has to be the SI unit, the joule. It has the merit that it is defined in terms of other SI units and does not have to be established experimentally. Energy is in fact “mass × acceleration × distance”, so a joule is defined as the quantity of energy needed to accelerate a mass of one kilogram at a rate of one metre per second squared over a distance of one metre.
All the other possible units listed above have disadvantages. The calorie is the amount of energy required to raise the temperature of 1 g of pure water from 14.5 °C to 15.5 °C at atmospheric pressure of 100 kPa. However, these conditions can only be reproduced in a controlled laboratory situation, and are not generally applicable. Similar objections apply to the British Thermal Unit, which is the amount of energy required to heat one pound of water by one degree Fahrenheit, which also makes it completely incompatible with other SI units. The electronvolt is appropriate for nuclear physics (albeit its value must also be determined experimentally) but it is far too small for normal use.
The “kilowatt hour” (kWh), as seen on electricity and gas bills, is an especially unsatisfactory unit. As we have seen, a watt is a joule per second. So a kWh is a kilojoule divided by a second multiplied by an hour. There are 3600 seconds in an hour, so a “kilowatt-hour” is in fact 3600 kJ – that is 3.6 MJ. So wouldn’t it be more sensible to measure the energy contained in electricity or gas in joules – or in this case, megajoules?
Since, as shown above, power is the rate of conversion of energy, the choice of unit for measuring power follows from the choice of unit of energy. “Horsepower”, with all its variants, is not a serious candidate since very few people could actually define it – except to say that an engine with a big number is more powerful than an engine with a small number. “British thermal units per hour” (BTU/h) are unsatisfactory for the same reason as the BTU is unsatisfactory. So it has to be the watt.
Not rocket science
The above relationships are not rocket science, and anybody within the normal intelligence range can easily understand them. So why aren’t they better known and used? I suspect a combination of reasons, such as:
- inertia – people are comfortable with what they are familiar with – so people carry on using different units to measure the same thing.
- the media dumb down to the lowest common denominator of understanding.
- ignorance of basic science (like not being good at maths) is tolerated and even considered fashionable by people who would not admit to ignorance of, say, Charles Dickens or the Battle of Trafalgar.
- mistaken beliefs that traditional “British” units (such as Fahrenheit!) have cultural value.
- fear of incomprehension or even ridicule from their peer group if units are used in an unfamiliar context – e.g. kW for measuring a car’s engine power, or metres in cricket or football.
How can these barriers to understanding be overcome? Basically, by increasing familiarity. Much depends on setting a good example – and this will depend on schoolteachers (especially outside the maths or science lesson), politicians (Tony Blair, to his discredit, did great harm by feigning ignorance of kilometres in 2006), broadcasters and journalists, role models in sport and show business. A lead from the Government would also help.
Reverting to the issue of “calories” on menus (which is where this article started from), it is quite deplorable that a Government agency – the Food Standards Agency – should have encouraged extended use of the unsatisfactory unit, the “calorie” (or did they mean “kilocalorie” or indeed “Calorie”?) instead of the proper SI unit, the joule. They even used the word “calorie” as a synonym for “energy”. In doing so, they are promoting ignorance and misunderstanding, and they are failing even to try to educate people to relate the energy they absorb in food and expend in their physical activity to the energy that is so wastefully used in transport, electricity generation and in domestic heating systems – to the detriment of our planet.