Hi, Kailee,
The US receives 2379 kJ/m^2 energy per hour. We need to multiply that by the total area in the US, which is 9,158,960 km^2. The problem is that one is expressed in km^2 and the other as m^2. So we need to convert one of the units. The question does not specify which unit it wants the answer to have, so I'm going to pick one - km^2, since the amount of energy is already large for a large area. But you could also pick m^2.
[I left out the "per hour" in these figures to keep it simple, and since the answer request per hour. But you could add this unit if the question asked for something like "over a 24 hours period. But, most places don't get 24 hours of continuous sunshine].
Since 1,000 m = 1 km, I can make a conversion factor that changes m^2 to km^2 by squaring both sides:
1,000,000 m^2 = 1 km^2, or 1xE6 m^2 = 1 km^2
Depending on what conversion I want, put divide one side by the other to produce either:
- 1xE6m^2/1km^2, or
- 1km^2/1xE6m^2
You'll agree that both reduce to a value of "1," since both the quotient and the denominator are equal. That means I am free to multiply them against any value, since they won't change the result, with the exception that the units will change.
Let's express the energy density as unit/km^2 instead of unit/m^2. That way I'll have a number that I can apply directly with the value of US area in km^2, so that the km^2 will cancel.
2379 kJ^m^2/(1000000m^2/km^2)
The m^2 cancel and the km^2 moves to the top. = 0.002379 kJ/km^2; the energy density in kJ per km^2.
Then we multiply the US surface area (in km^2) by this value to give the total energy per hour (assuming it's daytime :)).
0.002379 kJ/km^2 * 9188960 km^2 = 21789.17 kJ
We are limited to 4 significant digits, so the answer is 21,790 kJ.
This can be expressed in a larger unit, such as 217.9 GJ (gigaJoules) or 21.79 TJ (teraJoules).
[These numbers assume it is daylight, no clouds, no volcanoes, and no light reflect from aircraft. But I digress.]
