# Should the increasing energy retained in the atmosphere be considered in relation to global warming?

Atmosphere Energy

Heat energy is continuously being added into the atmosphere by the burning of fossil fuels.
It is in the form sometimes called “sensible energy”, and is just the kinetic energy of motion of all of the nitrogen, oxygen and other molecules in the atmosphere. This is not electromagnetic energy, and so it cannot be radiated away. Therefore, it builds up year by year during the many years of the anthropogenic activities, forming an aggregate of energy in the atmosphere, and a corresponding rise in temperature.

The nitrogen and oxygen in the atmosphere are diatomic molecules, and so the relationship between the energy of the atmosphere and its temperature on the Absolute Scale is given by the Kinetic Theory of Gases as follows.

E = (5/2)nkT where E is the energy in Joules n is the number of molecules k is the Boltzmann Constant, 1.381(10^-23) T is the Absolute Temperature, in Kelvin

So for changes, dE and dT, dE = (5/2)nk*dT

The BP Statistical Review of Energy provides data for the global annual energy consumption needs each year from all anthropogenic sources. I have summed this annual data numerically from 1980 to 2019 to calculate the total global sum, the aggregate, of the energy put into the atmosphere in this period. It is 1.783*(10^22) Joules.

However, both NASA and the IPCC maintain that 90.5% of this goes into the oceans, so from 1980 to 2019 the aggregate retained in the atmosphere by 2019 was 1.694(10^21) Joules.*

Now, the number of molecules in the global atmosphere is 1.04*(10^44), and so the equation from the Kinetic Theory becomes dT = dE / ( (5/2)nk ).

Therefore, dT = 1.694(10^21) / ( (5/2)1.04(10^44)1.381(10^-23) )

dT = 1.694(10^21) / 3.5906(10^21)

dT = 0.47 K (or degrees C) as at 2019, relative to 1980

This is in good agreement with measured temperature anomalies. It is not entirely clear whether or not the full number of molecules in the atmosphere should be used, because the effective distribution has not been considered. However, if only a smaller number are effective, then the resulting increase in temperature would be greater.

The explanation for atmosphere energy and temperature given above is simply basic Physics, and so the energy put into the atmosphere must be taken into account. It is often called the “primary energy”.

• I think you are referring to human-generated heat only, correct? You may want to reflect that in the title. Generally spoken, the energy reservoir the atmosphere provides -- similarly to the oceans -- must of course be taken into account. How much of the warming is due to human inputs is another question. Commented 2 days ago
• You might want to learn about thermal radiation - all matter with temperature will emit electromagnetic radiation. So your starting statement is false. There even is an atmospheric window which allows exactly that band of radiation to get to space. Commented 2 days ago
• -1 because the question is based on a false premise as @Arsenal pointed out. "This is not electromagnetic energy so it cannot be radiated away. Therefore it builds up year by year..." is not true. Energy is radiated from things that have temperature, regardless of how the heat was produced or transmitted.
– Mark
Commented 2 days ago
• @EddieBanner Sun > Earth: 170,000 TW; geothermal energy "flow" through Earth's surface: 45 TW; primary energy "flow": 18 TW (which is 0.034 W/m², if I've done the math right). In other words: your calculations are probably right, but only valid for a closed (or isolated) system (i.e. no energy flow through the boundaries of this system). Planet Earth is no isolated system, "Law of Conservation of Energy" - mentioned in another of your comments – is not affected. Commented yesterday
• @klanomath true, but you still have around 80 to 100 W/m² leaving the earth through infrared radiation. Commented yesterday