# Why is deodorant cold?

1. Jul 27, 2013

### Sweeney

Recently I was wondering why deodorant is cold when its comes out of the spray can. Some explanations say that it is because of a change in pressure. But looking at the ideal gas law T = PV/nR and both n and R are constant. And for every decrease in pressure there should be an increase in volume (Boyle's law:PV=constant). Therefore T should be constant.

The error in this logic could be that this only applies to ideal gases. If so, what property of the deodorant makes it act like this?

2. Jul 27, 2013

### Staff: Mentor

It will depend on the specific formulation, but chances are that the stuff is a liquid while it's the in the can (shake a half-empty can - does it slosh?) under pressure, evaporates when it's released. Evaporation absorbs heat from (that is, cools) the surroundings fairly quickly.

And of course the gas laws, whether ideal or not, don't apply to liquids or the liquid->vapor transition.

Last edited: Jul 27, 2013
3. Jul 27, 2013

### Staff: Mentor

Boyle's law doesn't apply here. Boyle's law ASSUMES that T is constant, so it cannot be used to show that T is constant. In fact, in order to keep T constant you generally have to have the gas exchange heat with some reservoir.

The gas goes through the nozzle of the can so fast that it does not have time to exchange heat with anything. So the proper way to think of this is as an adiabatic expansion (http://en.wikipedia.org/wiki/Adiabatic_process). In an adiabatic expansion there is no heat exchange.

Since the volume is increasing and since the pressure is non-zero that means that ΔPV is positive, which in turn means that the gas is doing work on the surroundings. The energy to do that work comes from the thermal energy of the gas, so the thermal energy of the gas decreases and therefore its temperature decreases.

4. Jul 27, 2013

### fluidistic

I'm curious if I'm getting the following right:
The gas escapes by the nozzle due to a difference of pressure (P being higher inside the bottle than outside). When the gas expands into the air, it is not a free expansion (because in a free expansion there's no air and the expansion costs no work and hence the temperature of the gas remains the same). The work that the gas does on the surroundings is basically done by pushing against the air molecules. The energy of the gas lost by doing so translates as a decrease in temperature. Is that correct?
So it's exactly the same as the case if I'm blowing air from my mouth?

5. Jul 27, 2013

### webboffin

Perhaps the same way a refrigerant works in a fridge

6. Jul 27, 2013

### Staff: Mentor

That is a good question. I don't know about expansion into a vacuum.

7. Jul 27, 2013

### 256bits

I would go with the evaporation ( Nugatory ) from the skin of the carrier fluid.

8. Jul 27, 2013

### Staff: Mentor

Ditto. Back in the day, they used to use CFC's as the propellant fluid, but now-a-days, I don't know. During the time that the CFC/0zone issue was prominent in the media, there was a book out called the Spray Can Wars. People who used spray can deodorants were considered environmentally irresponsible.

Chet

9. Jul 27, 2013

### rcgldr

One aspect not mentioned yet is that at the initial moment of spray, the temperature of the can has not yet decreased, and that the sprayed output isn't cooler until the temperature within the can has decreased due to expansion of gas and/or conversion of liquid to gas over a period of time.

The other part of this is that the spray itself could be getting cooled due to evaporation and/or reduction in pressure of the tiny droplets of the spray as it travels out the nozzle and through the air.

10. Jul 27, 2013

### fluidistic

According to wikipedia:
Here's a small study of coldburns: http://pediatrics.aappublications.org/content/126/3/e716.full.pdf+html, in which one can read

11. Jul 27, 2013

### SteamKing

Staff Emeritus
Stop worrying yourself to death. Switch to a roll-on deodorant.

12. Jul 27, 2013