So, you’re obsessed with implementing the perfect temperature controller for your Gaggia Baby Class (or Classic or any other derived model)1Oh, you’re not: is it just me then?. You’ve realised that you really need to know the values of some important parameters and the only easy way to get those is to take the boiler apart. And you don’t want to do that2Are you sure you don’t? If you do, you can take the opportunity to improve the brew head temperature.. The good news is I’ve done it for you3Where I also took the opportunity to improve the brew head temperature.. Here is everything you need to know4At least, I hope so: I don’t want to take it apart again.:
The boiler shell is made from 610g of aluminium. Specific heat capacity of ally is C=0.9J/g/K. So that’s 549J to heat the shell by 1°C.
The brew head is made (as far as I can tell from googling) from brass. Its mass is 1172g. For brass, C=0.38J/g/K. So 445J is required to heat the brew head by 1°C. (I’ve been a bit lazy here and included the shower screen and the ally plate it bolts to in this mass – so the numbers will be slightly wrong.)
[Update: in later experiments, I've added the brass portafilter into the brew head's thermal mass. This has a mass of 450g. The total heat capacity is now 616J/K.]
The internal volume of the boiler is 100ml. For water, C=4.216J/g/K. So you need 421.6J to heat the water by 1°C5The water, of course, expands as it heats and so 100ml is not always 100g. For my own model I have assumed an – erm - ideal water which does not expand.
It seems to me there are five thermal masses involved which all heat at different rates and which interact. The shell, water and brew head I have mentioned. Then there is the ambient air which cools the brew head and the casing and air cavity around the boiler which is heated by the boiler shell and cooled by the ambient air. The latter is of minimal concern if you’ve lagged the boiler (it contributes a loss of less than 20W when at brew temperature) – I have yet to determine its effects with an uninsulated boiler. The keen experimenter will want to know the heat transfer coefficients. My experimentally determined values are:
- About 3.3W/K for heat transfer from the shell to the brew head. i.e. for each degree difference between shell and brew head, heat is transferred at a rate of about 3.3W. (For the improved version with the heat-sink compound, it’s 3.6W/K). I assume most of this heat transfer is through the water, which must be quite turbulent with two surfaces of different temperatures adjacent to it in quite a small space.
- About 40W/K from the boiler shell to the water.
- About 0.5W/K from the brew head to the ambient air.
- Total loss from the boiler shell through the casing into the ambient air is around 0.2W/K with my lagged boiler. It will be higher than this with an uninsulated boiler and may be significant.
Finally, there’s the question of how the hotness gets into the machine in the first place. The heating elements have stamped into the side of them a label saying they each produce 680W at 120V. As they’re wired in series for UK models and mains voltage is nominally 240VAC, this means the boiler produces a nominal 1360W. Having said that, they also say 535W at 110V, which, bearing in mind that power is proportional to the square of voltage, implies 636.7W at 120V for a total of 1273W. Is there some inductance and an assumption that 110V comes at, say, 60Hz whereas 120V comes at 50Hz? I don’t know. I measure the resistance of the elements as 21.2Ω and 21.5Ω for a total power (assuming negligible inductance) of 1349W. So take your pick.
[ + ]
|1.||↑||Oh, you’re not: is it just me then?|
|2.||↑||Are you sure you don’t? If you do, you can take the opportunity to improve the brew head temperature.|
|3.||↑||Where I also took the opportunity to improve the brew head temperature.|
|4.||↑||At least, I hope so: I don’t want to take it apart again.|
|5.||↑||The water, of course, expands as it heats and so 100ml is not always 100g. For my own model I have assumed an – erm - ideal water which does not expand|