Calculations for cooling a volume of air

[Christina H]

Hallo,

Working on building a cloud chamber based on thermoelectric coolers rather than dry ice or other "consumable" cooling methods, and having some difficulty working out some of the numbers.

Say I have a volume of air at room temperature, for arguments sake 1600cm³, and I want to cool this volume down to, again for arguments sake -30*C.

Now, a simple look at it would suggest that a TEC with a dTmax of 70*C will be able to produce the temperature differential needed, but it also has a Qmax (watts of heat it can move). If there was no external influence on the volume of air we're trying to cool, we would surely arrive at that temperature difference at some point - higher cooling capacity would just reduce the time it takes. This all assuming the hot plate on the TEC itself is sufficiently cooled, but let's for now simply assume that it is.

But this isn't how it works in reality of course because this volume of air, even if encased inside a plexiglass container, is being heated by the outside atmosphere as well, which, is at room temperature. So there's some amount of heating occurring - the TEC has to do some amount of work. This work reduces the temperature difference it's able to produce.

What I want to figure out is what this amount of "work" the TEC has to do is, to arrive at my target temperature.TL;DR - How much cooling power do I need to bring a volume of air to a given temperature, if I have a known surrounding atmospheric temperature and a known heat pumping capacity. If this makes sense.

Any help would be appreciated, if there's any more information needed I should probably be able to provide it

 

[russ_watters]

Welcome to PF!

So you've honed-in on the needed piece of information without giving it: how much insulation does your chamber have?

 

[Christina H]

Thank you!

And, that's one of the slightly unknown things right now in the project, but the chamber atmosphere essentially is only insulated from the outside by a couple millimeters of Polycarbonate glass (let's assume 2mm thick). I presume the thermal resistance of polycarbonate glass and the thickness of it is a big part of the insulation you're asking for?

The material we'll be using is not 100% yet, we might just use good old glass, or we might use polycarbonate, but either way I can probably find the thermal resistance of that and adjust the numbers later.

The bottom of the chamber (to which the TEC cold plate is attached, from underneath) is a sheet of copper ~2mm thick. Not insulated further in any way - which brings me to another point, I guess it'd be a good idea to insulate the bottom floor of the chamber to increase the thermal resistance of the whole system.

I'm not sure if I actually provided you with any more useful information here, but that's all we know for now.