Friday, October 16, 2009

Climate Maths

Right, I'm getting fed up with this. This morning's metro has a quarter-page ad for the government's ACT ON CO2 campaign, explaining that I should use less water in the shower. Yes, water, that well-known carbon emitter.

According to this campaign's FAQ, "Over 40 per cent of CO2 emissions in the UK come directly from what individuals do – for example, using electricity in the home and driving cars. That means we can all make a difference. If every home can install 270mm loft insulation, it would save 3.8 million tonnes of CO2 – the same as the annual emissions of around 650,000 homes."

OK. Maths time!

A typical person breathes about 7-8 litres of air per minute, 11000 litres per day.[source]. Sanity checking, this means that a person would breathe all of the air in a lift once in a few hours, which seems plausible.

Using the ideal gas law, pV = nRT, we can calculate how much air this is in molecular terms. Pressure (p) is around 1 atm (by definition) or 100000 Nm-2. Volume (V) is 11m3. R is the gas constant, 8.31 Jmol-1K-1. T is the temperature, let's say 293K (20 degrees Celsius / 68 degrees Fahrenheit). Solving for n, we get 452 mol of gas.

The air we breathe out contains approximately 4% more CO2 than the air we breathe in.[source] This means that 18 mol of the gas is CO2. The reason for using the mole (~6.03x1023 molecules) as a unit is to simplify calculations: CO2 has a molecular weight of ~44 g/mol (12 for the carbon atom, 16 each for the oxygens) and so 18 mol of CO2 weighs 795g (1.75 lbs). Let's round that to 800g / 0.8kg as these calculations aren't accurate enough. That's on the same order of magnitude as the food and water intakes, so it seems plausible.

A typical person produces 800g (0.8kg, 1.75lbs) of CO2 per day.

Now, the fun begins. There were approximately 6,790,062,216 people in the world in July 2009. [source] A bit too much precision, there - let's call it 6.8 billion now. Multiplying 6.8bn people by 0.8kg/person/day and 365 days/year gives us 1986 million tonnes of CO2 per year. Can't really support four significant figures, so let's round it to 2000 million tonnes.

The human population of Earth produces 2000 million tonnes of CO2 per year simply by breathing.

Hang on, though. That rounding was 14 million tonnes! Let's go back to our ACT ON CO2 quote. A mere 3.8 million tonnes is the annual emissions of 650,000 homes, so that rounding error would be the emissions of 2.4 million homes - about a tenth of the UK. Wow!

Talking of those 650,000 homes, though... their 2.2 inhabitants will each produce 0.292 tonnes of CO2 per year, so 0.42 million tonnes of CO2 - 10% of their total emissions - is produced by respiration. Is that supposed to be scary? That we breathe as much CO2 as we waste through not having 9" thick loft insulation?

The government wants us only to emit 159 million tonnes of CO2 per year by 2050. Bit of a shame that the UK population exhales over 18 million tonnes of CO2 per year - more than 11% of the total.

Even more telling: the UK's entire current "carbon budget" - for power, transport, and everything else - is the same as the amount produced by the Chinese population simply breathing.

More than a tenth of the "damage" we do to the environment is through respiration; I'm inclined to think that such small multiples are irrelevant. Exercise and sex greatly increase respiration volumes - by more than a factor of 10.

Your breathing during heavy exertion, 150 litres/minute, accounts for more than twice as much CO2 production as everything else in your life put together - driving, flying, importing non-seasonal vegetables, technology, heat and light, etc.

How about we stop worrying about trivial amounts of CO2 and just get on with living?

- KoW

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