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A student was wondering how much an increase of energy a 2 degree change would be. This question is in context of climate change and the goals of the Paris Climate agreement. Obviously if we go to zero degrees Celsius we don't have absolute zero energy. So if the Earth's average energy goes up by 2 degrees from pre-industrial levels how much of a percentage increase is that to Earth's energy budget?
Question Date: 2018-01-30
Answer 1:

The heat content of the Earth’s atmosphere would increase by the amount
E= M *Cp* delta T

So the M is the mass of the atmosphere = 5 x 10 18 kg

Cp = heat capacity of air = 1000 J/kg K delta T = 2 K

Hence energy content increases by 10 22 Joules.

This assumes that the entire atmosphere increases by 2 Kelvin and that we ignore the T effect of Cp which is small.

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