Re: Cooling coke or beer

From: Gregory L. Hansen (glhansen_at_steel.ucs.indiana.edu)
Date: 09/11/04 

Date: Sat, 11 Sep 2004 12:39:28 +0000 (UTC)

In article <chulud$g4m@odbk17.prod.google.com>,
Stou Sandalski <stou.sandalski@gmail.com> wrote:
>
>John wrote:
>> How long time does it take to cool a certain volume of liquid in the
>> freeze?
>>
>> P dt = m c dT but how do I calculate P if all I know is the
>> temperature of the freeze, the initial temperature of the liquid and
>> the fact that it is air in the freeze. Approximations can be made
>> quite freely.
>
>Why don't you just time it? Depending on the specific heat capacity of
>the liquid, the shape of the container, the material of the container,
>its position in the freezer, other stuff in the freezer, and the
>cooling capacity of the refrigeration system the results will vary...
>
>You can experimentaly determine the specific heat capacity of beer or
>coke, but thats really not going to help you much.
>
>stou

Approximation: the temperature inside the liquid is uniform.

Approximation: the rate of heat loss is linear in the difference in
temperature. (This includes radiative cooling for small differences in
temperature.)

Approximation: the temperature of the heat sink is independent of the
temperature of the can, and independent of time. This includes the
boundary layer of air immediately surrounding the can.

Heat content of the can: dQ = m c dT

Rate of heat loss: dQ/dt = -k A (T - T0)

With A the surface area of the can, A=2*pi*r*h + 2(pi*r^2), T0 the
temperature of the heat sink, and k an empirical constant. Take the time
derivative of the first equation and substitute dQ/dt away. Start with an
initial temperature Ti.

  T(t) = T0 + (Ti - T0) exp(-kAt/mc)

Practical experience: About three hours in the refrigerator, half an hour
to an hour in the freezer. Liquid nitrogen will cool a can of Coke in
about 30 seconds. Experiment carefully, as you can easily cool the can
to the point that it will explode when you open it, and make a mess.
Except for liquid nitrogen, the fastest way to cool your beer is by
agitating it in a washing machine full of water and ice, except
thin-walled cans will have about a 30% casualty rate. 

-- 
"A nice adaptation of conditions will make almost any hypothesis agree
with the phenomena.  This will please the imagination but does not advance
our knowledge." -- J. Black, 1803.

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