Cooling beer faster with statistical mechanics

Classical Mechanics Level 3

Maxine and Warren invited Chloe to dinner, and told her to buy some beer along the way.

Diligently, Chloe buys a six-pack while on the way, but the store only has room temperature beer.

When she tries to apologize to Warren, he's not disappointed at all.

- It's ok - He says - I know how to make beer cool faster. With the power of science! -

He wraps each can in a wet cloth, then he puts cans in the freezer.

- Here we are, now they will cool much faster! -

Can you tell why the wet-cloth-wrapped-beer cools faster?

Because poured water is cold Because of evaporation of water Because water freezes below 0°C Because thermal conductivity of water is more than air's

1 solution

Simone Di Cataldo
Nov 9, 2015

Every freezer is not just cooled, it is also dehumidified.

If it wasn't, frost would be continuously be forming everytime the counter is open and closed, and outside air enters.

This means that the vapor pressure inside a freezer is kept at zero. In simple terms, this means that, when it's closed, there are no water molecules in the air of the freezer, because if there's any, it is taken away by the dehumidifier.

Before water freezes inside the cloth, molecules are moving because of thermal agitation, the faster they go, the "warmer" they are. In fact, in statistical mechanics, one can define the speed of a particle as $v_{avg}=\sqrt{\frac{2 k_{B}T}{m}}$

Where $T$ is statistical temperature , $m$ is the particle mass and $k_{B}$ is a constant. By reverting this relation we get $T = \frac{ m v^{2}}{2 k_{B}}$

This means that if a particle is faster, it is warmer from the point of view of statistical mechanics. But the fastest molecules jump away from the cloth, and there are no fellow molecules in the air to replace them, because they are taken away by the freezer. So the cloth (and the bottle with) is taken away the highest temperature particles .

Actually what we just described is evaporation, from the microscopical point of view. Evaporation is different from boiling, even if they are often confused in everyday life. Boiling water needs 100°C, but evaporation occurs at any temperature higher than 0°C, provided that the surrounding air has not reached the maximum allowed humidity yet (also called vapor pressure ). Anyway, evaporation is a phenomenon which needs energy to occur.

In this case.. energy can be only taken by beer's heat.

pssssssssssssch

cheers

Cooling beer faster with statistical mechanics

1 solution

0 pending reports