If you would use the heat from earth's core to run power plants, presumably by leading in water and running a steam turbine, wouldn't that eventually heat up the atmosphere since you pump out the heat in the core faster than it would naturally?
Waste heat radiates into space fairly readily, especially at night, so at the rate we currently use energy it’s not a significant factor compared to the incredible amount of heat that radiates down on us from the sun.
> Wouldn't the equilibrium temperature be both a function of energy in and radiation rate (which is also a function of temperature?)
Exactly, and since we're not changing the energy in (that energy is going to reach us whether we pump it up or not), and thus the equilibrium does not change.
Where else can all that generated energy go other than up?
My explanation would be correct if the earth is in equilibrium and there is no primordial heat left and all heat comes from radioactive decay, but surprisingly (to me at least) that is not the case. About 1/2 of the heat flow from the core to the surface comes from primordial heat.
I'd say solar will also add some heat to the atmosphere because they reflect less sunlight than the surface.
Of course, in the big scheme of things this is all pretty irrelevant unless we keep on exponentially increase our energy usage. The greenhouse effect of CO2 is a few orders of magnitude higher.
> The Earth receives 174,000 terawatts (TW) of incoming solar radiation (insolation) at the upper atmosphere [1].
> The flow of heat from Earth's interior to the surface is estimated at 47±2 terawatts (TW) [2].
Much of heat flux happens in ocean where crust is thinner.
> The Earth's crust ranges from 5–70 kilometres in depth and is the outermost layer. The thin parts are the oceanic crust, which underlie the ocean basins (5–10 km) [3]
Earth radius is 6,371 km, Earth core radius is 3,485 km, world deepest borehole is 12 km [4], they are not going to pump energy directly from the core.
World energy consumption is 18 TW [5].
We would live in a different world if balance was different. No seasons and climate zones if internal Earth energy was comparable to Sun energy. Tropics near power plants if human consumption was comparable to Sun energy.
[1] https://en.wikipedia.org/wiki/Solar_energy
[2] https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget
[3] https://en.wikipedia.org/wiki/Structure_of_Earth
However, it would be a very small increase to a very small source of heat. Underground heat in total is only about 0.03% of total energy budget at the surface.