Good to see UIC play a period without a goaltender.  I always felt
pulling a goaltender during a game could be used as a great tactical
weapon.  For example,  you get a good rush up ice under certain
circumstances, you pull the goalie to get the one-man edge.  If the team
is aware of the situation, they can compensate for his loss and, in my
opinion, more than make up for it by having the extra skater.  Then re-
insert the goalie with the next line change.
 
Now that the obligatory hockey content is taken care of, on to the real
purpose of this post.
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Hot water or cold water, which freezes first?
 
Let's start with the basics:
 
Suppose we have two cups of water, no tops, 100 g of water in each.
One has water at 25 C, the other at 100 C, pressure is 1 atmosphere.  (I
use the metric system because it's easier and the English system is
archaic.)
 
How much energy must be removed from each cup so each will have
the water turned to ice?
 
(/\ will be used as the symbol for "delta")
 
We use the equation   /\H = C /\T
 
For the cold cup, /\H = (1 cal/gK) * (100 g) * (25 K) = 2,500 cal
 
     also, the heat of fusion:  (100 g) * (80 cal/g)  = 8,000 cal
 
                                Gives a total of 10,500 calories.
 
Similarly, for the hot cup:
 
                /\H = (1 cal/gK) * (100 g) * (100 K) = 10,000 cal
 
     also, the heat of fusion:  (100 g) * (80 cal/g)  = 8,000 cal
 
                                Gives a total of 18,000 calories.
 
The hot cup needs to lose more heat, 7,500 calories more, so all things
being equal, or using lids on the containers, the cold cup will freeze
first.  But all things are not equal.
 
Next into play is the factor of evaporation.  The heat of vaporization for
water at 100 C is 540 cal/g.  In other words, with a difference of 7,500
calories, how much of the water would have to evaporate to make the
energy loss needed to freeze be equal for both cups?
 
This is tricky, because it is actually a related rates problem which I
don't have time to solve.  Both cups will lose mass due to evaporation,
but the hot cup will lose a lot more.  Get any amount of water to nearly
boiling point.  Put your hand over it and you'll feel steam.  Do you ever
feel the steam from a cup of water at room temperature?  I will estimate
this answer by dividing 7,500 calories by 540 cal/g, which gives a total
of 13.9 g, a good estimate, in my opinion.
 
In other words, if a little under 14% (or more) of the hot water
evaporates, that cup will freeze first because the remaining energy in
that cup will be less than the energy in the cold cup.  At this point the
evaporation of both cups would be about equal, but the hot cup will
have significantly less than 100 g, while the cold cup will still be close
to 100 g, and the smaller mass would win the race.
 
I believe more of the water will evaporate.  Next time at an arena,
watch the zamboni and see how much steam the water lets off.  Or, get
a pot of water almost boiling.  A lot of steam is coming off, and it
doesn't take long to boil water away when heat is applied.  The rate of
vaporization will be greatest just as this experiment would start, when
the water is very hot, the molecules are colliding and transferring
energy, and the amount of energy needed to vaporize would be at its
lowest.
 
I was certain this was correct when I made my original post for 3
reasons:
 
1.  I read about the experiment and how you can win bar bets with it.
 
2.  I saw a local newscaster (Steve Caporizzo, Channel 10 in the
Capital District) perform this on the science segment of the 5:30 news
once, back when Beth McKay was the host.  Because of her I watched
religiously.  She was going to bear my children.  Then she moved to
Texas and broke my heart, the b***h.
 
Sorry, I got sidetracked.
 
3.  I thought it through and I have supreme confidence in my reasoning
abilities.
 
Now, there will come a point where the hot water is not hot enough to
provide sufficient evaporation, and therefore the cold water will freeze
first.  But if you see steam, I'm confident you'll have hot water freezing
before the cold water.  However, the hot water will provide less ice,
since some of the water flew away.
 
Finally, to answer the obvious question of:
 
"Kurt, if I need ice, should I use hot water to make it as fast as
possible?"
 
The answer:  "No, go to the store and buy a bag of ice."
 
I'm done.
 
Kurt Stutt
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