I don’t know how to reason on the magnitudes and indirect effects here. If we are using the temperature differential, don’t we have to vent that into the atmosphere? Does that heat eventually go into the atmosphere anyway?
I am aware of the 2nd law. I am looking for data on the magnitudes involved. Every time there is a promise of very cheap energy, I wonder how we will deal with the waste heat.
The waste heat will be radiated away to space. The premise of global warming is that CO2 (and other "greenhouse" gasses such as methane) cause more of the heat to be retained in the atmosphere.
The magnitude is the same as current power sources that they would be replacing i.e. 100's of MWs to 1-10s of GWs. The amount of heat being brought up would have to be about the same as you would otherwise be getting from coal, gas etc and so the same amount of heat would be vent to the environment.
Geothermal will not be as cheap as solar, so if we use a lot more power, it will mostly be solar. (Geothermal would be used mainly for baseline, at night.)
Solar intercepts energy already arriving, to use before it is then re-radiated to space. It arrives regardless.
So, no problem. What we have now is a catastrophically big unfolding climate crisis. Even if there were a problem, any small problem is a wonderful substitute for a catastrophically big problem.
Global energy production in 2019 across all sectors was ~18TW. Excess radiative forcing from anthropogenic greenhouse gas emissions was ~560TW.
So we have room to ~20x our energy consumption before we start having to worry about climate change from direct heating, so long as we draw down the excess CO2 we've emitted.
Wind doesn't contribute to that total, as it's harvesting energy already in the system. Solar mostly doesn't contribute to that total, but it does increase surface albedo.
