Global Warming

Is global warming induced by human activity? What is the relationship between human energy output and atmospheric temperature increase?

Some would have you believe that we are all doomed if we don't cut our carbon emissions, because a 1 degree rise in temperature would raise sea level, wiping out coastal habitation. They claim that a majority of scientists agree that this is true.

Others discount these pronouncements, claiming that these theories are unproven and that the climate models on which they are based are both incomplete and not in agreement with observations.

So, armed with some basic facts, my trusty spreadsheet, and a knowledge of thermodynamics gained at great cost to the US taxpayer, I am going to explore the mathematics of this problem. This will probably take several posts.

First off, I want to know what the contribution of simple human existence is to the temperature of the planet. There are approximately 6.6 billion people on Earth right now, and we all generate heat just by living. The question is, how much heat, and what does that heat do to the atmosphere? Fortunately, the science of thermodynamics has figured out all kinds of cool ways to make these kinds of calculations.

The basic unit of energy is the Joule. The Wikipedia article I linked has a number of different conversion factors for Joules, but here are the most useful for this exploration:

1 joule in the real world is approximately:

• the energy required to lift a small apple (102 g) one meter against Earth's gravity.
• the amount of energy, as heat, that a quiet person produces every hundredth of a second.
• the energy required to heat one gram of dry, cool air by 1 degree Celsius.
• one hundreth of the energy a person can get by drinking a single 5 mm diameter droplet of beer.

So, a quiet person produces 100 Joules/second, which will heat 100 grams of dry cool air by 1 degree Celsius. Extending that to the entire population of the Earth, we produce enough heat energy every second to heat 660 billion grams (6.60x10⁸ kg) of dry air by 1 degree Celsius. That's a lot of heat!

So how much atmosphere are we heating? An estimate here puts the mass of the atmosphere at about 5,000 trillion metric tons, or 5.1480×10¹⁸ kg.

If we assume perfect conduction of human-produced heat energy into the atmosphere, then we can just divide the mass of the atmosphere by the mass-temperature rise each second to get the time it would take basic human existence to increase atmospheric temperature by 1 degree Celsius.

5.148 x 10¹⁸ kg / 6.6 x 10⁸ kg per sec = 0.78 x 10¹⁰ sec

7,800,000,000 seconds to heat the atmosphere by 1 degree Celsius equates to:

• 130,000,000 minutes
• 2,166,667 hours
• 90,278 days
• 247 years

So, if we assume (as above) that the atmosphere is a perfect receiver of heat, and that none of it goes into other things (like heating up the ocean), then in about 250 years the air will be 1 degree Celsius warmer (on average) due to the mere fact of human existence. This timeline doesn't support many of the claims, so the energy that is raising the temperature of the atmosphere must be coming from something other than basic human metabolism.

Next up: Raising the temperature of the ocean.