Wonderment Question: If you buy a cup of coffee off campus, but want to wait until you get to class

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Wonderment QuestionIf you buy a cup of coffee
off campus, but want to wait until you get to
class to drink it, which is better - adding the
cream right away when you buy it, or adding it
later, right before you drink the coffee?
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Research leads us toNewtons Law of Cooling

• Rate of cooling for a hot body is proportional to
  the difference in temperature between the bodys
  temperature and the temperature of its
  surroundings - ?T/t k?T
• This results in an exponential decay curve of
  temperature change over time

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How we propose to test this?

• Start out with a container of hot water.
• Take the temperature at regular intervals with a
  thermometer.
• At varying times add in a small amount of cool
  water.
• See how this affects the resulting temperature.

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Prediction/Initial Theory

• Is it better to add cool water right away?
• Is it better to add the cool water at the later
  time?
• Or does it not make a difference either way?

Jim and I think that the later we add the cool
water, the hotter the resulting temperature of
the liquid will be. We based this on our
understanding of Newtons law of cooling. We base
this prediction on our understanding of Newtons
Law of Cooling which states that the rate of
cooling is proportional to the difference in
temperature. So we think that if you add the
cool water when the hot water is hotter it will
drop the temperature more than if you add it
after the hot water has cooled. (Plus, it just
intuitively seems right to add the cream later.)
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Getting to do actual Science
Very fun and exciting!!
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Control run (w/o adding cool water)
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Inconclusive Results
First Run
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If we knew what we were doing, it would not be
called research, would it?
-Albert Einstein
An Experiment Modified

• Used a cooler temperature for liquid added, 13?
  vs. 23
• More cool liquid was added 40ml vs. 20ml
• One thermometer was used
• Improved techniques were learned from our first
  run
• Beer Food Happy Researchers

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Second Run
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The Claim
In order to ensure a warmer overall liquid
temperature, you should add a cool liquid to a
hot liquid at the earliest possible time.

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The Evidence
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Four Varying Time Trials, or Is it true for all
times?
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Oh Those Assumptions

• We assumed that coffee reacts to Newtons Law of
  Cooling the same as water. (the literature
  supported this)
• We assumed that a small amount of cool water
  would react similarly to cool cream when we added
  it to the coffee or hot water.
• We theorized and thus assumed, but did not have
  time to test that our claim holds true for any
  container, as we only tested in a glass beaker.
  (Again, this is supported in the literature and
  is taken into account somewhat by the constant k
  in Newtons Law of cooling. But of course the
  cooling graph will be much flatter for a better
  insulated container.)

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Dump in the Creamer ASAP!!!!!

• We have determined that the sooner you add a cool
  liquid to a hot liquid the higher the temperature
  of the resulting liquid mixture.

• In order to better understand this, we revisited
  Newtons Law of Cooling and we believe that we
  initially misled ourselves. We now believe that
  it makes sense that it is better to have the
  greatest temperature change at a point on the
  decay curve where the rate of cooling is greatest

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Another way of looking at why adding sooner is
better

• There are two things that happen when you dump
  the cool water into the hot water
• The temperature of the hot water immediately
  drops - and the hotter the water is, the greater
  the temperature drop will be.
• The rate of cooling slows down - and the sooner
  you slow down the cooling rate the warmer the
  resulting water will be.
• The second behavior (item number 2) turns out to
  be more important and has a larger impact on the
  final resulting temperature.