Extra heat gets added out of nowhere when using Thermo Aquatuner

Question

Problem Statement

I decided to test my understanding of heat exchange and temperature handling in Oxygen Not Included. So I used Sandbox and Dev Mode to set up a simple heating loop and then tried to calculate the resulting temperature of the liquid I was heating.

Alas, the lab test results diverged from my calculations by a lot. I would appreciate any help finding flaws in my reasoning.

Lab Setup

Design

Pipes

Wiring

Heating

All the materials inside the box started at 10.0 ℃.

Then I fed 4 kg worth of Super Coolant at -35.1 ℃ to the Thermo Aquatuner.

As expected the coolant got cooled by exactly -14.0 ℃ down to -49.1 ℃.

Calculations and Expected Result

Insulated Tiles of the box are made of Insulation which has Thermal Conductivity of 0.0. This means the box itself cannot heat up or cool down, it also perfectly insulates its contents preventing any heat exchange between the insides and the outsides.

As an extra measure to prevent unwanted heat exchange, the area outside of the box is a vacuum.

So, since neither the box itself nor the vacuum outside of it could exchange heat I assumed that all the heat "extracted" from the coolant should go to the insides of the box.

Here's the inventory of the box contents:

• 1 Thermo Aquatuner made of Thermium with a mass of 1200 kg
• 1 piece of Conductive Wire made of Thermium with a mass of 25 kg
• 2 pieces of Insulated Liquid Pipe made of Insulation with a mass of 400 kg each
• 2 cells of Polluted Water with a mass of 1 kg each
• 2 cells of Water with a mass of 1 kg each

Insulated Liquid Pipes are made of Insulation, so they don't participate in the heat exchange.

For the reference, here are the properties of the materials exchanging heat:

Material	Specific Heat Capacity, DTU/g/℃	Mass, kg
Water	4.179	2
Polluted Water	4.179	2
Thermium	0.622	1225
Super Coolant	8.440	4

1. Heat required to heat up an object is the product of material's heat capacity and temperature change:

   ΔQ = C × ΔT

2. Heat capacity is the product of specific heat capacity and mass of the material:

   C = c × m

3. Temperature change is the difference between the final temperature and the initial temperature:

   ΔT = T_final − T_initial

4. Given the formulae above the amount of heat given by the coolant is this:

   ΔQ_{super coolant} = c × m × (T_final − T_initial)

   ΔQ_{super coolant} = 8.440 × 4 × (−49.1 − (−35.1))

   ΔQ_{super coolant} = 8.440 × 4 × (−14)

   ΔQ_{super coolant} = −472.64 kDTU

   Note, the result is negative because the coolant is cooled instead of heated.

   Also note, it's kDTU not DTU since mass is in kg not in g.

5. Since the system is closed (no heat is received from the outside, none is dissipated either), the heat amount stays the same, in other words the heat change is zero:

   ΔQ_{super coolant} + ΔQ_{box contents} = 0

   ΔQ_{box contents} = −ΔQ_{super coolant}

6. Assuming we give the system enough time to stabilize, the initial temperature of the box contents is going to be the same for all its parts such as pipes, wires, liquids, devices, etc. The same applies to the final temperature.

   Therefore we can treat the box contents as a single pseudo-object that has some heat capacity, so having formula (1) in mind we get the following:

   ΔQ_{box contents} = C_{box contents} × ΔT_{box contents}

7. Heat capacity of the box contents is the sum of heat capacities of its parts:

   C_{box contents} = C_{thermo aquatuner} + C_{conductive wire} + C_water + C_{polluted water}

   C_{box contents} = m_{thermo aquatuner} × c_thermium + m_{conductive wire} × c_thermium + m_water × c_water + m_{polluted water} × c_{polluted water}

   C_{box contents} = (m_{thermo aquatuner} + m_{conductive wire}) × c_thermium + m_water × c_water + m_{polluted water} × c_{polluted water}

   C_{box contents} = (1200 + 25) × 0.622 + 2 × 4.179 + 2 × 4.179

   C_{box contents} = 1225 × 0.622 + 2 × 4.179 + 2 × 4.179

   C_{box contents} = 761.95 + 8.358 + 8.358

   C_{box contents} = 778.666 kDTU/℃

8. Now starting from the formula (6) and substituting formulae (3), (5), (4) and (7) we can derive the final temperature of the box contents:

   ΔQ_{box contents} = C_{box contents} × ΔT_{box contents}

   ΔT_{box contents} = ΔQ_{box contents} ÷ C_{box contents}

   T_{box contents final} − T_{box contents initial} = ΔQ_{box contents} ÷ C_{box contents}

   T_{box contents final} = ΔQ_{box contents} ÷ C_{box contents} + T_{box contents initial}

   T_{box contents final} = −ΔQ_{super coolant} ÷ C_{box contents} + T_{box contents initial}

   T_{box contents final} = −(−472.64) ÷ 778.666 + 10.0

   T_{box contents final} = 472.64 ÷ 778.666 + 10.0

   T_{box contents final} ≈ 10.6℃

So the conclusion is that after the box contents get heated and all its contents parts take their time to balance the temperature the final temperature of the box contents would be 10.6℃.

Actual Result

And here's the actual results that I got in the game:

The actual temperature is 12.8℃ instead of 10.6℃ calculated above.

I would appreciate any clues as to where I made a mistake in my calculations.

Answer 1

One oddity in the game is that buildings have their mass divided by 5 when calculating specific heat.

Cbox contents = (1200 + 25) × 0.622 + 2 × 4.179 + 2 × 4.179

Cbox contents = 1225 × 0.622 + 2 × 4.179 + 2 × 4.179

Cbox contents = 761.95 + 8.358 + 8.358

Cbox contents = 778.666 kDTU/℃

This now becomes

• Cbox contents = (1200 + 25) ÷ 5 × 0.622 + 2 × 4.179 + 2 × 4.179
• Cbox contents = 169.106 kDTU/℃

Finishing your math:

• Tbox contents final = −(−472.64) ÷ 169.106 + 10.0
• Tbox contents final = 472.64 ÷ 169.106 + 10.0
• Tbox contents final = 12.7949333554℃

Answer 2

Insulated Tiles of the box are made of Insulation which has Thermal Conductivity of 0.0.

This small part is wrong and leads to an incorrect calculation. Insulation does not have a thermal conductivity of 0.0, it has a thermal conductivity of 0.00001 (as per the wiki you linked). Unfortunately the game rounds this number and displays 0.0 instead.

The same applies to the Insulated Liquid Pipes. They participate in the heat exchange, but just very very little.