Scout's post about 156TW of lost heat energy had me thinking... there's no time component on that so I'm assuming it's just a constant? As long as the sun is shining on something on earth, it's getting X watts. When it's not shining, it's getting 0 watts.
Given that X - 1.3 = 999X/1000 (a translation of "Total solar output reaching the surface varies by just 1.3 Watts per square metre (0.1 percent) between the maximum and minimum phases of the cycle"), that means that:
X - 1.3 = 999X/1000
1000X - 1300 = 999X
X - 1300 = 0
X = 1300
The sun delivers 1300 watts per square meter of earth, and varies by 1.3 watts during max/min cycles.
120 trillion square meters yields 156,000 trillion watts of juice. Getting lazy and dividing by half (the sun only shines on half the planet at a time, right? Well, not really and not with full intensity) that means that the planet really only gets 78,000 trillion watts for 24 hours a day, or 78,000TWh per hour. A variation of 0.1 percent, or 78TWh, is accounting for a dip in planetary temps.
In a year, the sun bestows on us 28,470,000 TWh
Total world electrical generation in 2009 (wikipedia's latest data) suggests mankind creates 20,000TWh total in a year.
The sun dumps 1423.5 times the amount of energy we produce, into our atmosphere, our oceans, our land and our crops, than we do. Almost 100% of that is in the form of heat.
Question:
Given 20,000TWh of power generation per year and an average electrical efficiency such that 75% of that power is converted to heat as either resistive waste or intent, and given that the volume of the earth's atmosphere is 4.2 billion kilometers... how much could 15,000TWh of waste heat warm 4.2 billion kilometers of air?