# Aquatuner and steam turbine efficiency should depend on temperature

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A heat pump has a maximum theroetical possible efficiency due to the first law of thermodynamics.  This efficiency is called the coeffecient of performance.  It has a simple formula:

COP for cooling = Tcold / (THot - TCold).

TCold is the final temperature of the coolant, THot is the temperature of the aquatuner.  Temperatures are in Kelvin.

If you are cooling water to 10 celcius (283 kelvin), and the aquatuner is at 24 celcius (297 kelvin)
COP = 283 / (297 - 283) = 20.  This means 1200W of electricity could transfer at most a huge 12,000W of heat from the cold water to the slightly warmer aquatuner.

If you are cooling water to 10 celcius (283 kelvin), and the aquatuner is in hot steam at 125 celcius (398 kelvin).
COP = 283 / (398 - 283) = 2.46.  This means 1200W of electricity could transfer at most 2952W of heat from the cold water into the steam turbine.  It becomes 5 times less efficient than the above aquatuner.  Probably not worth using it to power a steam turbine.

If you are cooling supercoolant to 1 Kelvin in a steam turbine at 125 celcius (to make liquid hydrogen).
COP = 1 / (398 - 1) = 0.02.  This means 1200W of electricity could at most transfer 24W of heat.  It becomes 5000 times less efficient than the first aquatuner.

I think if COP was added to aquatuner efficiency the physics simulation would be improved greatly and would help teach players about thermodynamic laws.  And it would be more obvious why you cannot cool anything to below absolute zero.

For the steam turbine the maximum possible efficiency is this formula:
Efficiency = 1 - (TCold / THot)

If the steam turbine is at 90 celcius (363 Kelvin), and the Steam is at 125 celcius (398 Kelvin).
Efficiency = 1 - (363 / 398) = 0.08 (8%).  1200W of heat energy could at most be converted to 96W of electricity, with the rest heating up the turbine.

If the steam turbine is at 90 celcius (363 Kelvin), and the Steam is at 900 celcius (1173 Kelvin)
Efficiency = 1 - (363 / 1173) = 0.7 (70%).  1200W of heat energy could at most be converted to 840W of electricity.

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I don't disagree however this is beyond the scope of ONI and their goals for modeling real world systems.

For instance pressure changes do not change the temperature of gases in ONI as it would be too computationally intensive.

Aquatuners cool items by a set number of degree. Meaning that using a liquid with a greater heat-capacity nets you more energy removed for the same amount of electrical power consumed.
This is already a very unrealistic system for heat transfer. They would first need to actually change the amount of temperature change in each fluid rather than it being a constant amount.

Also the net power from aquatuner to steam turbine is already negative. The steam turbines just help as magic heat deletion and to recover some power.

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On 12/26/2020 at 3:36 PM, Nocare said:

Also the net power from aquatuner to steam turbine is already negative. The steam turbines just help as magic heat deletion and to recover some power.

I believe it’s only negative until you get supercoolent.  Then it becomes just about neutral.  (Not sure if higher or lower)

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On 12/28/2020 at 3:00 AM, Lupbert said:

I believe it’s only negative until you get supercoolent.  Then it becomes just about neutral.  (Not sure if higher or lower)

I just did the math on that: -55W per AT. It's consistent with what the wiki says.

@deuteros The AT is a mysterious device that reduces the temperature of the coolant, regardless of the thermodynamics involved. I don't understand what exactly bothers you... but my memories of Physics 101 are turning in their graves (where they belong) more because the -14C drop happens no matter of the SHC of the material or the mass involved.  The AT happily drops by 14C 10kg of supercolant  or  1g of Molten Lead for the same 1200J.

I guess we have to live with the fact the ONI is only a game that doesn't not even attempts at simulating real world physics.

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On 12/19/2020 at 8:27 AM, deuteros said:

I think if COP was added to aquatuner efficiency the physics simulation would be improved greatly

Nope!

ONI is a perfect physics simulation. Literally perfect. It has to be, it's a coded game.

What it isn't is a model of our universe (which should be obvious).

So with that out of the way: Why? What gameplay does it add? Especially given the added complexity and thus increase to minimum system requirements it would produce to be implemented.

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Note that Carnot efficiency is for an idealized engine operating infinitely slowly.  Real world engines use a different formula

1 -  squareroot( (THot - TCold) )

That significantly lowers your efficiency for Steam Turbines and the like.  Refrigerators also suffer reduced performance but the formula is not clear to me.