Wikipedia Affiliate Button
24 May 2009
17 May 2009
29 March 2009
21 September 2008
07 September 2008
13 July 2008
22 June 2008
08 June 2008
25 May 2008
30 March 2008

Equalling the Sun

This is a companion article to the one on transformity. It is filled with figures and simple calculations. I have provided links for all the important figures such as how much energy there is in oil and how much comes from the sun. It's purpose is to show how, even with modest growth rates, we could demand as much energy as the sun is giving us in a matter of centuries. I wrote this article before the one on transformity, so in reposting it I have removed almost all the commentary as it's adequately covered in the one on transformity.

The Mtoe is a unit of measure used in the oil industry. It is an acronym for Millions of tonnes of oil equivalent.

From this site we discover that: 1 Mtoe = 4.1868 x 1016 J
This accords closely with another figure (1 TJ = 0.0002388 Mtoe) I found here.

From the British Petroleum site you may download statistics on world energy usage in the Excel spreadsheet format.

From the Primary Energy Consumption sheet we discover that 10537.1 Mtoe of energy was consumed in 2005. This is equivalent to 4.4116 x 1020 J. Thus the power output of the entire world in 2005 was:

4.4116 x 1020 J / (86400 s/day * 365 day) = 1.3989 x 1013 W

From Wikipedia we discover that the solar constant is 1366 W/m2. The Earth has a cross section of 1.274x1014 m2. Thus the power received by the Earth is 1.740x1017 W.

Thus the amount of power received from the sun was a factor of 12400 times larger than the entire power generated by humanity in 2005. This sounds like a lot of energy doesn't it? One is tempted to think that this is more than enough energy for humanity, more than we can ever use.

The same BP spreadsheet tell us that in 1965 world energy usage was 3863.1 Mtoe. It is now 2.728 times as large as that. We can calculate the average growth rate easily.

(1 + g)40 = 2.728
g = (2.728)(1/40) - 1 = 0.0254 = 2.54%

Now we are in a position to see how long it would take for the power generated to be equal to that of the power received by the sun. At the same growth rate of 2.54% we come up with the follow equation where n is the number of years.

(1.0254)n = 12440

n = log 12440 / log 1.0254 = 376 years

Has the growth rate slowed all that much in recent years? Last year it was 2.39%. Over the last 10 years it has averaged 2.09%. So to give a reasonable lower and upper bound I've provided the following table on how long it would take to equal the power received by the sun for various growth rates.

Growth rate Years
0.5% 1890 years
1.0% 948 years
1.5% 633 years
2.0% 476 years
2.5% 382 years
3.0% 319 years
3.5% 274 years
4.0% 240 years
4.5% 214 years
5.0% 193 years

And finally, to truly astound you, I have decided to answer a further question. How long would it take to demand all of the Sun's energy, not just that which falls upon the Earth's surface. Wikipedia tells us that the amount of energy falling on Earth is about one two billionth of that which the Sun outputs: 3.86 × 1026W. At the same modest growth rate of 2.54% we find that we could achieve this power generation in 1233 years.