# Calculations for cooling a volume of air

• Christina H
In summary, you would need a chamber that is at least two millimeters thick in insulation, and have a copper bottom to increase the thermal resistance.

#### 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

Welcome to PF!

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

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.

## 1. How do you calculate the required cooling capacity for a volume of air?

The required cooling capacity for a volume of air can be calculated by multiplying the volume of air (in cubic feet) by the temperature difference between the desired air temperature and the current air temperature. This calculation is represented by the formula: Q=1.08 x V x (T2-T1), where Q is the cooling capacity in BTUs, V is the volume of air in cubic feet, T2 is the desired air temperature in degrees Fahrenheit, and T1 is the current air temperature in degrees Fahrenheit.

## 2. What is the difference between sensible and latent heat in air cooling calculations?

Sensible heat refers to the heat that is required to change the temperature of a substance without changing its state, while latent heat refers to the heat that is required to change the state of a substance (such as from a liquid to a gas) without changing its temperature. In air cooling calculations, both sensible and latent heat must be considered in order to accurately determine the required cooling capacity.

## 3. How does humidity affect air cooling calculations?

Humidity plays a significant role in air cooling calculations as it directly affects the latent heat of the air. Higher humidity levels mean that there is more moisture in the air, which requires more energy (in the form of latent heat) to cool the air. Therefore, a space with high humidity levels will require a higher cooling capacity compared to a space with lower humidity levels.

## 4. Can the type of cooling system affect the calculations for cooling a volume of air?

Yes, the type of cooling system can affect the calculations for cooling a volume of air. For example, a refrigeration system uses a different cooling capacity calculation compared to an air conditioning system. Additionally, different types of cooling systems may have varying levels of efficiency, which can also impact the required cooling capacity.

## 5. How do you determine the appropriate air flow rate for cooling a volume of air?

The appropriate air flow rate for cooling a volume of air can be determined by dividing the required cooling capacity by the specific heat of air (0.24 BTU/lb°F). This calculation will give you the required mass flow rate of air in pounds per hour. From there, you can determine the appropriate air flow rate based on the specific air velocity required for your cooling system.