How long would it take for boiling water to cool to the following
temperatures? (all degrees in fahrenheit)
165
170
180
200
All measurements should be done in a 47oz kettle.

For example, if I boil water in a tea kettle, how long would it take
to reach 180 degrees after I take it off the heat? 1 minute, 2
minutes, 2 minutes and 30 seconds, 10 minutes?

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Request for Question Clarification by answerguru-ga on 15 Jul 2006 13:21 PDT

Hi coos-ga,

In order to answer this question it is also necessary to provide the
temparature in the environment around the kettle (ambient
temperature). Obviously if you stick your kettle in a sink full of
cold water it will cool far quicker than if you just left it in room
temperature :)

Let me know and I can calculate this for you.

Cheers,
answerguru-ga

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Clarification of Question by coos-ga on 15 Jul 2006 16:01 PDT

The environment would be room temperature

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Request for Question Clarification by welte-ga on 08 Aug 2006 15:28 PDT

Hi coos-ga, Are you talking about idealized "47 oz. of water" at
standard temperature and pressure, without regard to the kettle and
such?

   -welte-ga

*Boiling* water cools at exactly the same rate at which it is being
heated. It is at thermal equilibrium, and its temperature remains at
the boiling point until the source of heat input is removed. :)

Good point!

But yes...to answer the question you MUST provide an ambient
temperature.  Room Temp isn't precise enough ... is the room in Tahiti
or the North Pole?

Also...where in the water are we measuring the temperature?  Is the
surface not going to cool faster than the middle of the water?

And the dimensions of the jug matter as well. Is it tall and skinny or
short and fat.

And the composition of the kettle.  Is it insulated?  Is it Aluminum,
Copper, Steel.

etc etc.

There are alot of variable yet to define.

Here are some notes for you to review including a piece on Newton's
Model of Cooling.

http://www.math.montana.edu/frankw/ccp/modeling/simple/winter/body.htm

Wowza - $100 to answer this question?  Yikes!  

To know exact values, one would also need to know the dimensions of
the kettle.  I know it's 47 oz, but a proverbial "spherical kettle"
will behave differently than a "very large but shallow" kettle. 
Surface area is the important factor here.

What's the altitude where you are?  Unless you're at sea level, or
reasonably close to sea level, your boiling water will not be at 212
degrees.  For instance, where I grew up in Colorado, water boiled at
just a smidge under 200 degrees!  Barometric pressure will also (to a
much smaller amount) affect your boiling water temperature.  The 212
degree value assumes a standard atmosphere, meaning 1013.2 millibars
of pressure and at sea level.

Also, what material is the kettle composed of?  I'd assume steel, but
I've seen kettles in plastic (the electric ones), aluminum, copper,
ceramic, etc...

Next, where are you placing the kettle?  What will the bottom be in
direct contact with?  If you're hanging the kettle, for instance, then
it would be in direct contact with air.  If you're placing the kettle
on a cold metal table, results will vary.

Finally, will the lid be left on the kettle, is it one of the whistle types, etc.

All that information will play a vital role in determining the
temperature/time information you are looking for if you want to solve
analytically to a high degree of accuracy.

An easier solution:  buy a thermometer and measure the water
temperature at 1, 2, 3, or 5 minute intervals.  You can then form
yourself a plot of water temperature vs time for your specific kettle
and your specific conditions.  The whole experiment shouldn't take
more than an hour and at the end, your data will be much more accurate
than any analysis could hope to be.

I forgot to mention that also, Relative Humidity will also be an
important factor, unless your kettle is sealed.  The drier it is, the
more water will evaporate from the kettle, causing cooling due to
evaporation, which means two things...1) your water will cool faster,
and 2) since some of the water evaporates, you now have less water in
your kettle, so your water will cool faster.

Another thing:  how much water is in the kettle?  It is 47 oz of
fluid, or is that just the advertised kettle size?

Your question refers to boiling water and temperatures that are below
the temperature at which water boils at atmosphetic pressure (1014.25
mbar).

If the water is to continue to boil at these lower temperatures then
the gas pressure on its surface must have been reduced. The water will
boil until it has lost sufficient heat to freeze, after which it will
sublime. If it is not to freeze then heat must be added. There is no
mention of any added heat, ie take it off the fire then puting it back
on again which would change the time taken to reach any given
temperature.