So...bachelors in physics here. I believe I have a reasonable grasp physics (no promises), and I at best might understand what's being attempted with the EM-water situation.
As I understand, we're attempting to create a cycle of:
- use EM to cool air to temp A (where A is some set amount lower than ambient)
- use that air to cool water to temp A
- after EM fades use that water/ice to cool the air to temp A and call that the new ambient temp so we can start at step 1 again
The conversation seems to be on how to interpret or model how EM works so it's reasonable that Isan didn't work out EM nukes or arbitrarily low temps (if those are even possible).
I'm gonna say that this whole thing can be bypassed by simply saying that step 2 from above doesn't really work regardless of how you model EM.
The specific heat capacity of water is ~4 times greater than that of air, meaning that if everything is magic and:
- the air-water system only exchanges energy internally, and
- we ignore that the air and water would reach a thermal equilibrium before the water is cooled, and
- the air-water energy transfers always works at 100% efficiency
we're still having to cast EM 4 times for every cycle.
For the first issue, in the non-magical world, the air-water system isn't thermally isolated. If we're not in an enclosed building, the air will lose most of it's energy to non-cooled air surrounding it, or from just drifting away from the water. Since that's not useful, we'll assume that we're doing this in an enclosed building or something. The air will still lose most of it's coolness to the walls and ceiling. The water/ice will also be losing coolness to whatever it's resting on when we have it unsealed. Given the technology of the MfD world to thermally isolate a very large room, lets be generous and call this 10% efficiency (realistically closer to 5%). This means that we're up to casting EM 40 (80) times for one cycle.
The second issue is that the transfer of energy won't happen the way we want. If you had two cups of water, one hot and one cold, and put them in contact, they don't do what we'd like and transfer all energy from the hot one to the cold one. They reach an equilibrium, meaning each casting of EM will have only a fraction of the effect we'd expect. Under absolute best (magical) conditions, this will be an efficiency loss of 50%. Let's again be extremely generous and assume that's constant for our cycle (it's not and will absolutely get worse). We're now at 80 (160) casts of EM per cycle.
The third problem was given at the end of the second problem: the loss isn't constant, it get's worse. Energy transfer between systems that have a high temp difference happens efficiently and quickly. As that temp difference lowers (like our temp A air and our approaching temp A ice), so does the efficiency, massively increasing the time it takes for the transfer to happen and leaving more time for our coolness to be lost to the walls of our building. Meaning that the final stages of moving our ice to temp A have an efficiency approaching zero. Being incredibly generous (which definitely absolutely doesn't correlate to laziness on my part), we'll say this effect means 100% efficiency when we start and 0% when we end, and is linear throughout. Meaning another efficiency loss of 50%. We're now at 160 castings per cycle if we're being generous, and 320 if we're being closer to realistic.
This is of course a simplification. Things like the third issue can be mitigated a lot by not bringing the ice all the way to temp A, and instead only halfway to A, doubling your cycles but making each one more efficient. Still I think this demonstrates that if the QM's rule favorably, arbitrary temps could theoretically be achieved, but realistically they can't regardless of how the QM's model EM.
