# Effect of ambient pressure on newton cooling (water)

If I have a laboratory water bath (circulated for homogeneity in temp) that I will monitor over a period of time (probably 2 scenarios, an hour at most, and then at least 24 hours or longer), how do I quantify the effect of atmospheric pressure in our test lab.

What I will do is use an immersion circulator heater to raise the temperature to some value, then time how long it takes for each drop in one degree as an assessment of "ambient cooling power". This will be used as a background to subtract from the cooling or warming power of some device we will introduce into the water.

assuming a low biot number (which I think is reasonable) I believe I can use Newtons cooling law to "correct" for those times based on different ambient temps, ie the cooling from 60 to 59 to 58 to 57 degrees will differ depending on the ambient temperature, by working out the "alpha" constant in the exponential term as representing the specific physical parameters of the setup. So it seems like it should be straight forward to say if we measure a curve in a 20 degree room, what variation we can expect if the room is 21 or 22 degrees.

but what I cant see is where the effect of atmospheric pressure comes in, it seems like it must be "baked" in somehow to the constants forming the exponential term (heat transfer, area of surface, mass and spec heat of body), which I guess is the heat transfer term then

but is there any good way to calculate or estimate how to correct for variations in pressure since it will be difficult in practice to achieve specific ambient pressures "to order".

For the shorter measurements I can probably just assume a constant pressure and use the exponential term to provide a corrected set of times for arbitrary temps around the normal lab temp

but for the longer measurements I think the pressure will change quite a bit, it would be good to know the proper way to quantify that in a similar way.

hope this makes sense

mfb
Mentor
The pressure influences the air density by a few percent at most. I wouldn't expect a measurable effect from this. Different humidity should have a stronger effect on the heat capacity. If your water tank is open evaporation will be important as well.

yes, this water tank will probably be open (but not for sure). Humidity could be a factor, this is for verification and validation of a prototype medical device, so the documentation needs to be quite careful stating the test conditions used and the range of test conditions where our stated tests are still valid. It might be possible to just state a humidity and pressure range and say "neglible effect" but it would be nice to fully understand the relevant physics equations to see where this might or might not be a problem.
I was hoping it would not be a huge factor (probably we can state the test being done in a large room. the lab bath is about 30 x 30 cm in area with about 20L water.

some of the tests will be based around timing of cooling to atmosphere vs repeating but adding an external probe which will change that cooling rate (in other words its kind of "background" corrected)