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Many years ego, Earth was hot. Over time, it has lost energy and has become colder. Is it now in equilibrium or is its total energy changing?

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Check your local weather forecast to confirm that atmospheric temperature is not constant. – David H Dec 2 '13 at 17:07
@DavidH: Local weather is irrelevant to the question (which is about the total energy in the earth system). Heat can move from one area to another without affecting the total. Also, anyone interested in this question would probably also be interested in the Area51 Earth Sciences proposal – naught101 Feb 25 '14 at 23:40
@naught101 But it's absolutely relevant to the question of equilibrium, which is what I was addressing. – David H Feb 25 '14 at 23:46
@DavidH: hrmm. Yeah, you're right, I was misunderstanding the definition of equilibrium. Is there a word for when the earth system has no net heat exchange with the rest of the universe? Something along the lines dynamic equlibrium (in chemistry)? – naught101 Feb 26 '14 at 0:12
up vote 13 down vote accepted

"Total energy of the Earth" is somewhat of an odd concept, but there's no reason we can't really entertain it. It brings up some genuinely difficult questions. The right way to approach this is to define the system correctly and then identify forms of energy content and flows.

Things to "count" in the Earth's energy:

  • Heat content
  • Nuclear energy
  • Rotational energy
  • Gravitational energy

As I look at this list, I believe that all of them are steadily decreasing. Nuclear decays in the Earth's core continue over time, and this converts nuclear energy into heat content. I've heard that nuclear decay comprises a large fraction of the geothermal energy conducting through the crust, so it follows that the nuclear energy is declining at a similar rate as the heat content.

The rotational energy is constantly being transferred to the moon slowly, and this is similar to the maximum theoretical tidal energy that could be extracted.

Heat energy, of course, is lost by blackbody radiation to space. Global warming "blankets" our planet a little more, so it would initially decrease this. However, the heat content of the oceans and biosphere (which have the capability to absorb this energy) are small compared to the total Earth. There has always been a deficit between Earth's radiated energy and the sun's incoming energy which is from the nuclear and thermal energy of the planet.

Earth has always been on-net losing energy to space by radiation. An increased greenhouse gas could theoretically change this, and cause the Earth to keep more of its heat. However, it's small compared to Earth's natural flows. Perhaps after some past super-volcano the Earth temporarily gained energy. However, that's certainly not the case today.

I will point out a slight fallacy in the question:

Many years ego earth was hot and over time has lost energy and has got colder.

If normal heat content was the only store of energy, this would be a logical connection. Losing energy would mean lowering temperature. However, other stores of energy are present, notably rotational, nuclear, and gravitational. The conversion of these into thermal energy is strange. Rotational turns into tidal heating, and then contributes to the radiation deficit.

Nonetheless, if the Earth is taken as a whole, only the large center should matter significantly. That has almost certainly gotten cooler over time, in addition to releasing stored nuclear energy. If nuclear heat production was large enough, or if the mantle was insulating enough, it could have increased temperature because the heat from nuclear decay wasn't dispelled to the surface fast enough.

Venus, for instance, may have had cycles where the planet stored up extra energy, and then an event where the mantle went through a massive volcanic shift.

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Thank you for your answer. Does the energy radiated from the sun increase the mass of the earth? Also I know that in/outgassing also might change the mass (and hence energy) of the earth. Are these factors negligible? – Paul Dec 2 '13 at 21:05
@Paul Earth's energy is decreasing, so this reduces its mass by $c^2$ times that. The sun's radiation is an inflow matched by the outflow. Good call on the outgassing. I only looked at the energy balance. The sun gives the Earth protons, but Earth also loses protons to space while gaining meteorites. Here's one graph I made on that subject – Alan Rominger Dec 2 '13 at 21:27
A nice graph indeed. Thanks for the perspective on the mass decreasing by c^2 and the various other gains/losses – Paul Dec 3 '13 at 1:10
Do meteor impacts add any significant energy to the Earth system you defined? – KeithSmith Dec 3 '13 at 3:39
@KeithSmith It's small, here's my argument: the size distribution of asteroids places most of the mass locked up in the largest bodies. That means, for instance, the KT extinction event asteroid likely carried more energy than all the rest combined (like Ceres' mass). It was 100 million megatons TNT, which is small on the scale we're talking about. – Alan Rominger Dec 3 '13 at 12:16

The heat generated from the Earth's core is about 4x10^13 W while the Sun provides about 1.7x10^17W so although the Earth's core is slowly cooling this has very little effect on the Earth's temperature.

The Earth is in equilibrium between the energy received from the sun and the energy it emits into space. If the amount received changes, then temperature of the Earth will change to keep equilibrium - whether this is due to the sun emitting more or a more greenhouse atmosphere absorbing more.

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I'd say depends on the definition of 'total energy' - see Alan's answer above.

The total thermal energy is not in equilibrium, it is increasing: global warming, that is an imbalance of around 0.5 W/m^2, corresponding to a total imbalance of 2.5x10^14 watts (if I did the multiplication correctly...)

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Temperature increase doesn't imply energy increase. How do you come to that conclusion? – jinawee Dec 2 '13 at 17:12
@jinawee: why temperature increase doesn't imply energy increase? – MiMo Dec 2 '13 at 17:37
(note also that 'global warming' is first an energy imbalance at the surface, the temperature increase is an effect of it) – MiMo Dec 2 '13 at 17:42
Other types of energy (rotational, nuclear...) could decrease. See AlanSE's answer. – jinawee Dec 2 '13 at 17:42
"Global warming" lives in the troposphere which makes up a nearly vanishing fraction of the earth's mass and heat capacity. It is pretty important to us, but to the Earth as a whole it is a minor surface perturbation. – dmckee Dec 2 '13 at 17:51

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