morse@leadsv.UUCP (Terry Morse) (05/23/85)
There has been a discussion in net.cooks (of all places) of whether
or not it is possible to freeze hot water faster than cold water, all else
being equal.
There have been several explanations as to why it might happen. Some
people have even done experiments. I would like to pose this as a problem
and see if anybody has a solution. I want to know under what conditions
hot water will freeze faster than cold.
The energy transport mechanisms to consider are:
1) evaporative heat loss (and evaporative mass transfer)
2) convective heat loss (consider h = constant to simplify)
The container should be thought of as a rectangular cube with the top
side exposed to the air (your basic ice cube tray). As a start, think
of the following relationships:
mass loss = f ( T difference, surface area, humidity )
convective loss = f ( T difference alone (simplification) )
A simple form of the differential equation may be written in the form
outflow - inflow + change in storage = 0, or:
q(conv) + q(evap) + c d/dt( M Tw ) = 0
q(conv) = convective heat loss rate = h (Tw - Ta)
q(evap) = evaporative heat loss rate = ?
M = mass of water
c = specific heat of water (assume constant)
Tw = temperature of water
Happy gedanken experimenting!!!
--
Terry Morse (408)743-1487
UUCP: { (ucbvax!dual!sun) | (ihnp4!qubix) } !sunncal!leadsv!morse
UUCP: { allegra | ihnp4 | dual } !fortune!amdcad!cae780!leadsv!morsematt@oddjob.UUCP (Matt Crawford) (05/31/85)
In article <455@leadsv.UUCP> morse@leadsv.UUCP (Terry Morse) writes: >There has been a discussion in net.cooks (of all places) of whether >or not it is possible to freeze hot water faster than cold water, all else >being equal. > >There have been several explanations as to why it might happen. .... (This is an excelent argument for increased funding of science instruction at the elementary school level.) Assumption: The temperature of an object never takes a sudden jump, it varies continuously, although in some cases the change is rapid. Then consider two samples of water, one hot and one cold. At some time the hot sample will cool down to the initial temperature of the cold water. How will it then freeze faster than the cold water? You might argue that some of the hot water will have evaporated and that under some con- ditions the initially hot water could then freeze faster due to its lesser volume, but then I will say that "a given size ice cube can never be formed more quickly from hot water than from cold." _____________________________________________________ Matt University crawford@anl-mcs.arpa Crawford of Chicago ihnp4!oddjob!matt
gv@hou2e.UUCP (A.VANNUCCI) (05/31/85)
>>There has been a discussion in net.cooks (of all places) of whether >>or not it is possible to freeze hot water faster than cold water, all else >>being equal. >> >>There have been several explanations as to why it might happen. .... > >(This is an excelent argument for increased funding of science >instruction at the elementary school level.) > >Assumption: The temperature of an object never takes a sudden jump, >it varies continuously, although in some cases the change is rapid. > >Then consider two samples of water, one hot and one cold. >At some time the hot sample will cool down to the initial >temperature of the cold water. How will it then freeze >faster than the cold water? You might argue that some of >the hot water will have evaporated and that under some con- >ditions the initially hot water could then freeze faster >due to its lesser volume, but then I will say that "a given >size ice cube can never be formed more quickly from hot >water than from cold." A few years ago the Scientific American column "The Amateur Scientist" discussed the issue of whether hot water freezes sooner than cold water under certain conditions (e.g. when washing your car in subfreezing temperatures). The conclusion was the following: Obviously, if you use distilled, de-gassed water in a sealed container, the cold water will reach freezing point and start freezing before the hot water. However, "real-world" water (the stuff that comes out of you bathroom faucet) contains plenty of dissolved gases and other assorted dissolved junk. Water that has been heated has lost much of the dissolved gases and other stuff, so that if evaporation is the primary cooling mechanism (such as when you are washing your car) those few extra cal's may not be sufficient to counteract the faster evaporation rate and hot water will indeed freeze faster than cold water. Giovanni Vannucci AT&T Bell Laboratories HOH R-207 Holmdel, NJ 07733 hou2e!gv