What an appropriate username!
P1V1 / T1 = P2V2/T2
Volume remains constant, so with a reduction in pressure, temperature decreases.
I don't think the amount of moles decreased, since that would mean the amount of coolant molecules decreased as well. As per wikipedia, the liquid coolant releases heat when going through the phase transformation, lowering the overall temperature of the coolant accordingly.But that equation isn't valid since the moles of gas has decreased too. But after some thought I'm still leaning towards the pvnrt equation since if you drop pressure around water (causing it to boil) I don't recall the water being very cold. But I really could've sworn that phase changes from liquid to gas was endothermic in this case. It's been too many years out of school
NOTHING defies physics. If something appears to do so, then you need to modify your understanding of physics to explain the behavior you observe.
I don't think the amount of moles decreased, since that would mean the amount of coolant molecules decreased as well. As per wikipedia, the liquid coolant releases heat when going through the phase transformation, lowering the overall temperature of the coolant accordingly.
What's coolant have to do anything? When you use a duster, compressed air goes out, thus less molecules of whatever it was in the can.
You have no concept of a control volume do you? The number of molecules inside the can + the number ejected from the nozzle is exactly equal to the number of molecules in the can before you did anything.
The molecules that left the can underwent a phase change, where the number of molecules undergoing the phase change is exactly equal to the number of molecules that left the can. Yes, it's circular, that's the point!
It's obvious something expanded in the process. Then all you do is follow PV=nrT --> PV=T
Of course, this isn't all exactly right because you have the partial pressure step in between. Assuming that the can is held upright, any gas leaving was actually a gas while it was in the can, and the volume that was displaced by the leaving gas was filled by liquid inside the can changing to gas. However, as long as there is still liquid left, the pressure in the can will remain exactly the same (for a given temperature) and the number of molecules leaving will be equal to the number undergoing a phase change.
Edited in another line that you may have missed, but it's not relevant to your question:
"There are secondary effects caused by the decrease in liquid volume, thereby increasing the gas volume, that will cause more molecules to change state than actually leave, but we will ignore that for our first class"
To determine where most of the cooling is from you actually have to do all of the math out. There something called the enthalpy of phase change where when something changes state it either gains or loses energy from the environment. To determine the total energy change you must also know the partial pressures where the two phases can coexist (vapor pressure), from that pressure you can determine the delta_P to the atmospheric pressure and determine the temperature (energy) change from the gas expansion.
