[math-fun] Chinese tea puzzle
I pour a cup. It's too hot and too weak. With chopsticks I remove the bag from the pot and dunk it repeatedly in my cup. Will my tea cool faster if I dunk up and down rapidly, or pause several seconds between immersions? --rwg
* Bill Gosper <billgosper@gmail.com> [May 28. 2016 14:51]:
I pour a cup. It's too hot and too weak. With chopsticks I remove the bag from the pot and dunk it repeatedly in my cup. Will my tea cool faster if I dunk up and down rapidly, or pause several seconds between immersions? --rwg
This is the type of question the I asked (and got asked) as a student. So I have a go. Assumptions: The dipping goes in negligible time and the bag gets the temperature of the tea in negligible time. Then the high-frequency method cools faster as the heat flow is governed (linearly) by the temperature difference. By my assumptions you increase the surface and it is of tea temperature. The "slow" approach would allow a part of the surface be colder (thus less heat flow). Realistically the vaporization drives much more than linearly and that should make the "fast" method even better. Amirite?
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Have you tried putting it in the 'fridge? WFL On 5/28/16, Joerg Arndt <arndt@jjj.de> wrote:
* Bill Gosper <billgosper@gmail.com> [May 28. 2016 14:51]:
I pour a cup. It's too hot and too weak. With chopsticks I remove the bag from the pot and dunk it repeatedly in my cup. Will my tea cool faster if I dunk up and down rapidly, or pause several seconds between immersions? --rwg
This is the type of question the I asked (and got asked) as a student. So I have a go.
Assumptions: The dipping goes in negligible time and the bag gets the temperature of the tea in negligible time.
Then the high-frequency method cools faster as the heat flow is governed (linearly) by the temperature difference.
By my assumptions you increase the surface and it is of tea temperature. The "slow" approach would allow a part of the surface be colder (thus less heat flow).
Realistically the vaporization drives much more than linearly and that should make the "fast" method even better.
Amirite?
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_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
When I'm in a hurry to drink my too hot tea, I just add cold water. -- Gene From: Fred Lunnon <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Saturday, May 28, 2016 6:26 AM Subject: Re: [math-fun] Chinese tea puzzle Have you tried putting it in the 'fridge? WFL On 5/28/16, Joerg Arndt <arndt@jjj.de> wrote:
* Bill Gosper <billgosper@gmail.com> [May 28. 2016 14:51]:
I pour a cup. It's too hot and too weak. With chopsticks I remove the bag from the pot and dunk it repeatedly in my cup. Will my tea cool faster if I dunk up and down rapidly, or pause several seconds between immersions? --rwg
This is the type of question the I asked (and got asked) as a student. So I have a go.
Assumptions: The dipping goes in negligible time and the bag gets the temperature of the tea in negligible time.
Then the high-frequency method cools faster as the heat flow is governed (linearly) by the temperature difference.
By my assumptions you increase the surface and it is of tea temperature. The "slow" approach would allow a part of the surface be colder (thus less heat flow).
Realistically the vaporization drives much more than linearly and that should make the "fast" method even better.
Amirite?
* Fred Lunnon <fred.lunnon@gmail.com> [May 28. 2016 16:34]:
Have you tried putting it in the 'fridge? WFL
Too high tech! For someone who hates drinks being very hot, likes coffee, is impatient, and doesn't want ice cubes (too much hassle, alters taste), I dug up an aluminium rod, about 15 mm in diameter and 15 cm in length. You only need to dip that into the drink _shortly_ to get the temperature you want. Cue happy pal.
[...]
On 5/28/16, Joerg Arndt <arndt@jjj.de> wrote:
* Fred Lunnon <fred.lunnon@gmail.com> [May 28. 2016 16:34]:
Have you tried putting it in the 'fridge? WFL
Too high tech!
Not at all --- by the time you have finished puzzling over this, your tea has gone cold anyway! https://en.wikipedia.org/wiki/Mpemba_effect WFL
For someone who hates drinks being very hot, likes coffee, is impatient, and doesn't want ice cubes (too much hassle, alters taste), I dug up an aluminium rod, about 15 mm in diameter and 15 cm in length. You only need to dip that into the drink _shortly_ to get the temperature you want.
Cue happy pal.
[...]
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A *silver* "tea spoon" duh's the trick just fine; watch out not to burn your fingers on said spoon. https://en.wikipedia.org/wiki/Silver "[Silver] however, possesses the highest electrical conductivity, *thermal conductivity,* and reflectivity of any metal." At 07:48 AM 5/28/2016, Joerg Arndt wrote:
* Fred Lunnon <fred.lunnon@gmail.com> [May 28. 2016 16:34]:
Have you tried putting it in the 'fridge? WFL
Too high tech!
For someone who hates drinks being very hot, likes coffee, is impatient, and doesn't want ice cubes (too much hassle, alters taste), I dug up an aluminium rod, about 15 mm in diameter and 15 cm in length. You only need to dip that into the drink _shortly_ to get the temperature you want.
Cue happy pal.
[...]
Thermal conductivity at 25 C in W m^-1 K^-1 Silver 429Copper 401Diamond 2200C-12 enriched diamond 3300 -- Gene From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Saturday, May 28, 2016 10:03 AM Subject: Re: [math-fun] Chinese tea puzzle A *silver* "tea spoon" duh's the trick just fine; watch out not to burn your fingers on said spoon. https://en.wikipedia.org/wiki/Silver "[Silver] however, possesses the highest electrical conductivity, *thermal conductivity,* and reflectivity of any metal." At 07:48 AM 5/28/2016, Joerg Arndt wrote:
* Fred Lunnon <fred.lunnon@gmail.com> [May 28. 2016 16:34]:
Have you tried putting it in the 'fridge? WFL
Too high tech!
For someone who hates drinks being very hot, likes coffee, is impatient, and doesn't want ice cubes (too much hassle, alters taste), I dug up an aluminium rod, about 15 mm in diameter and 15 cm in length. You only need to dip that into the drink _shortly_ to get the temperature you want.
Cue happy pal.
Most "science and cooking" texts recommend flipping a burger or steak as often as possible. Same principle, I believe. The strength of tea wrt steeping time seems similar, though I don't know the relevant constants. What is the half-life of tea? Hilarie
I pour a cup. It's too hot and too weak. With chopsticks I remove the bag from the pot and dunk it repeatedly in my cup. Will my tea cool faster if I dunk up and down rapidly, or pause several seconds between immersions? --rwg
Your tea is mainly cooled by evaporation (breaking hydrogen bonds), rather than conduction (to the air) or radiation (into space). You therefore want to maximize the surface area accessible to the tea — your second option. Have you tried pouring the tea onto a cookie sheet (with rim)? -Veit
On May 28, 2016, at 3:11 AM, Bill Gosper <billgosper@gmail.com> wrote:
I pour a cup. It's too hot and too weak. With chopsticks I remove the bag from the pot and dunk it repeatedly in my cup. Will my tea cool faster if I dunk up and down rapidly, or pause several seconds between immersions? --rwg
participants (7)
-
Bill Gosper -
Eugene Salamin -
Fred Lunnon -
Henry Baker -
Hilarie Orman -
Joerg Arndt -
Veit Elser