Furnace temperature and pressure math

The data used was collected in version 0.2.2800. It was obtained with regular furnaces only, the advanced furnace is untested. If there is any difference between them, it would probably be the internal volume, the regular furnace holds 1000 L.

Furnace behaviour

• Only the gas inside the furnace have temperature, the furnace itself does not and absorbs no heat
• Combustion will consume 95% of the limiting ingredient, O2 or H2 (if there is 10 mol O2, and excess H2, 0.5 mol O2 will remain afterwards)
• Reaction formula: 1 O2 + 2 H2 -> 6 CO2 + 3 X + 595kJ
• No side reactions with other gases have been observed so far

Using perfect 2:1 fuel

Temperature peak

• T(after) = (T(before) * 61.9 + 0.95 * 595k) / (243.6 * 0.95 + 61.9 * 0.05)
  • Temperature in Kelvin (Celsius + 273)
  • 61.9 = heat capacity before combustion (based on reaction formula, so 3 moles total) = sum(specific heat * moles of each gas before) = 21.1 + 2*20.4
  • 243.6 = heat capcity for gas after combustion = sum(specific heat * moles of each gas after) = 0.05*(21.1 + 2*20.4) + 0.95*(6*28.2 + 3*24.8)
  • 0.95 and 0.05 refers to the 95% combustion efficiency
• The number of moles combusted doesn't matter under perfect conditions, the temperature increase is the same since the reagent/product ratio determines this outcome. The number of moles will however effect how quickly the gas cools.

Pressure peak

• P = nRT/V
  • n = total moles
  • R = 8314
  • V = 1000
• P (before) = n(before) * 8314 * T(before) / 1000
• P (after) = n(before) * (0.05*1 + 0.05*2 + 0.95*6 + 0.95*3) / (1 + 2) * 8314 * T(after) / 1000

Using diluted fuel

Unreactive gases (like an excess either O2 or H2) can be added before the ignition to increase pressure and decrease temperature. A benefit from doing this is a slower cooling rate. The outcome can be calculated like this.

Temperature peak

1. O2 moles reacted = min(moles O2, moles H2 * 0.5) * 0.95
2. released energy = O2 moles reacted * 595k
3. heat capacity (before) = sum(specific heat * moles of each gas (before))
4. heat capacity (after) = heat capacity (before) + O2 moles reacted * 181.7†
5. thermal energy (before) = temp (before) * heat capacity (before)
6. thermal energy (after) = thermal energy (before) + released energy
7. temperature (after) = thermal energy (after) / heat capacity (after)

† 181.7 comes from 243.6 - 61.9 (the change in the heat capacity for the gas before and after combustion, see above)

Pressure peak

1. total moles (before) = pressure(Pa) * 1000 / (8314 * Temp (before)
2. total moles (after) = total moles (before) + O2 moles reacted * 6†
3. Pressure (after) = total moles (after) * 8314 * Temperature (after) / 1000

†6 comes from 9 - 3, combustion consumes 3 moles and produces 9 moles

Using Ice(Oxite) and Ice(Volatiles)

There is a minor difference between which ice is added first. One can also observe a fluctuation in the combustion efficiency compared to when a furnace is fueled with gas. The end result also matters a little bit on how fast the ignition button is pressed when the first ice type is added while doing larger batches.

small batch, oxite first

• Adding 1 oxite + 1 volatile, in that order
  • Temperature: 2222K, Pressure: 2.03MPa, moles of O2/H2 combusted: 11/21, Combustion ratio (H2): 95%
• Adding 1 oxite + 2 volatiles, in that order
  • Temperature: 2514K, Pressure: 4.13MPa, moles of O2/H2 combusted: 22/43, Combustion ratio (H2): 98%

small batch, volatiles first

• Adding 1 volatile + 1 oxite, in that order
  • Temperature: 2224K, Pressure: 2.03MPa, moles of O2/H2 combusted: 11/21, Combustion ratio (H2): 95%
• Adding 2 volatiles + 1 oxite, in that order
  • Temperature: 2432K, Pressure: 3.93MPa, moles of O2/H2 combusted: 21/42, Combustion ratio (H2): 95%

large batch, oxite first

• Adding 5 oxite + 10 volatiles, in that order
  • Temperature: 2463K, Pressure: 18.76MPa, moles of O2/H2 combusted: 96/190, Combustion ratio (H2): 86%
• Adding 8 oxite + 16 volatiles, in that order
  • Temperature: 2537K, Pressure: 33.28MPa, moles of O2/H2 combusted: 172/344, Combustion ratio (H2): 98%

The difference in combustion efficiency is a mystery. Fuel temperature doesn't seem to matter (seen by furnace tests with 2:1 gas on both Mars and Europa). One possibility is that this deviation is a result of multiple consecutive ignitions. Whatever the reason, using ice in a furnace creates some unpredictability.

Furnace cooling rate

unknown

Observations

• the rate of cooling is temperature dependent, hotter cools faster (furnace temp - surrounding temp? how do vaccum behave?)
• the rate of cooling is time dependent (game tick speed is once per 0.5 seconds)
• the rate of cooling is mol dependent (small amounts cool faster, appears to be a linear correlation)
• adding ores decreases the temperature (do melting cost energy? or is this just from heating the trapped gases inside the ore?)

Possible experimental setup to measure dT/dt

• Hold a tablet with an atmos cartridge in the right hand (so it can be read when the game is paused). Aim the tablet against the furnace and pause with ESC, double tap ESC to move the game forward one tick, record the temperatures.
• Remember to record the total amount of moles as well

Resetting the furnace

Since only gas have temperature, evacuating all gas means resetting the temperature

Experiment used to determine the amount of released energy from combustion (so it can be verified)

1. Place a frame, build a furnace partially inside the frame, complete the frame. The furnace is now perfectly insulated and will no longer loose temperature (unless ore is added) nor explode from high pressure
2. Add fuel (2:1 not required) via a pipe, use over 1000 mol of O2, remove the pipe attached to the furnace
3. Record all mol amounts and temp with a tablet (atmos cartridge), convert temp to K (add +273)
4. Ignite furnace, record all mol amounts and temp with tablet, convert temp to K
5. Calculate moles of combusted O2 (= moles before - moles after)
6. Calculate the Thermal energy in the gas, before and after (Thermal energy = Temp * sum(mol of each gas * specific heat)
7. Calculate energy released per mol of combusted O2 (= TE.after - TE.before) / moles of combusted O2)
8. Deconstruct the furnace completely to disarm it safely, or connect a single pipe so it can burst and act as a vent
9. Alternatively: A circuit can probably also be used to capture the temperature and pressure at the point of ignition