Does pressure affect heat transfer between two mediums?

Question

I'm a self-taught Coca-Cola connoisseur and try to use science to be able to have the best taste possible in every glass. I usually try to get the bottles as cool as possible before opening them. I've noticed that when I open a bottle too soon (not cool enough yet), and then put it again to cool down, it does so faster than a bottle that has been in the refrigerator without interruption. This, however, is just empirical and I've not taken exact measures or data.

To make it more explicit, take two bottles of Coca-Cola that start off at room temperature. Let $t=0$ be the time they are put inside to cool down and let's say the wanted temperature is $0$°C:

• Bottle 1 is put in the refrigerator and cools down from room temperature to $0$°C in $t_1$ seconds.
• Bottle 2 starts the same but is opened before it reaches $0$°C, a glass is poured and then the bottle is closed again and put back inside. It then reaches $0$°C at, seemingly, $t_2 < t_1$ seconds.

It would be safe to assume the initial pressure inside the bottles is always greater than $1$ atm. When opened, Bottle 2's internal pressure goes down and it also loses around $200$ml of liquid. Does the difference of pressure between the inside of the bottle and the refrigerator affect the heat transfer and the time the bottle takes to cool down? Could it be another physical phenomenon that explains this (such as the loss of liquid)? (Am I making this up?)

Answer 1

Yes, gas pressure affects the rate of heat transfer to or from a gas, but that's not what you're measuring.

What's probably going on:

If you've poured $200mL$ out of the bottle, the remaining liquid will cool faster, because the rate of heat transfer is roughly proportional to the surface area, while heat capacity is proportional to the volume. Surface area varies as the $2/3$ root of volume, so if you multiply the volume by a factor of $0.8$, you multiply the volume by $0.8^{2/3}$, and so the cooling time is multiplied by $0.8/0.8^{2/3} \approx 0.93$.

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A pressure-related effect that is happening, but may be too small to measure:

When you open the soda, releasing the pressure, the dissolved carbon dioxide molecules boil out of the liquid. This is an endothermic process, so the liquid is cooled: heat flows from the liquid into the gas to pay for the phase change. I have no idea how much gas is released, but suppose it's somewhere on the order of 1 L from a 1L bottle being opened for a few seconds for the first time, which seems about right for how much they can froth over. Then that's about 2 g of CO2 , which has a latent heat of vaporization of about 700J, or about 1/5 of a degree worth of heat from your liter of water.

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A pressure related effect that isn't happening:

As I said at the beginning - yes, gas pressure affects heat transfer to the gas. If you isothermally pressurized your freezer, the rate of cooling would increase because density increases the conductivity of air. This isn't what's happening here, of course, but it's a direct answer to your question so I didn't think I should leave it out. The effect on cooling rate for the kinds of pressures that wouldn't be life-threatening would be negligible.

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If you actually want to cool the beverage quickly, just immerse it in a bucket of ice water. It'll cool rapidly to 0 and won't freeze.

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EDIT - oops! I wrote exothermic when I meant endothermic. Fixed.