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| coffee |
 Posted: Wed Jan 26, 2005 2:44 pm |
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Guest
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I have two identical, normal, coffee cups.
I have some milk, at 4 degrees Celcius.
I have some water in a kettle which has just boiled.
I pour a little bit of milk in mug A, and then add water.
I pour water into mug B (no milk).
Which mug will cool to 60 degrees Celcius first, and why?
Or does the Mpemba Effect say that I don't know until I experiment, because
the water, mugs, etc all have an effect? |
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| Uncle Al |
| Posted: Wed Jan 26, 2005 3:37 pm |
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Guest
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coffee wrote:
[quote:a60022fc1f]
I have two identical, normal, coffee cups.
I have some milk, at 4 degrees Celcius.
I have some water in a kettle which has just boiled.
I pour a little bit of milk in mug A, and then add water.
I pour water into mug B (no milk).
Which mug will cool to 60 degrees Celcius first, and why?
Or does the Mpemba Effect say that I don't know until I experiment, because
the water, mugs, etc all have an effect?
[/quote:a60022fc1f]
All other things being equal, rate of thermal conduction depends on
thermal gradient.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf |
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| CWatters |
| Posted: Wed Jan 26, 2005 3:55 pm |
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"coffee" <coffee@dnac48.dabsol.co.uk> wrote in message
news:Xns95EAC7CB8C67A28762153tmichanet@ptn-nntp-reader04.plus.net...
[quote:07a1e81aa9]I have two identical, normal, coffee cups.
I have some milk, at 4 degrees Celcius.
I have some water in a kettle which has just boiled.
I pour a little bit of milk in mug A, and then add water.
I pour water into mug B (no milk).
Which mug will cool to 60 degrees Celcius first, and why?
[/quote:07a1e81aa9]
A: Mug A with milk
In effect you start off with two mugs full of similar liquids but one is
slightly cooler than the other. The cooler one (Mug A) will reach 60 first.
Why? Because both mugs cool down at roughly the same rate and mug A has a
"head start".
That all assums a) it's only a little milk and mostly water in A and b) that
the outside temp is < 60C... |
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| relay61:13:214:23 |
| Posted: Wed Jan 26, 2005 4:03 pm |
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Guest
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"coffee" <coffee@dnac48.dabsol.co.uk> wrote in message
news:Xns95EAC7CB8C67A28762153tmichanet@ptn-nntp-reader04.plus.net...
[quote:0701cb6cab]I have two identical, normal, coffee cups.
I have some milk, at 4 degrees Celcius.
I have some water in a kettle which has just boiled.
I pour a little bit of milk in mug A, and then add water.
I pour water into mug B (no milk).
Which mug will cool to 60 degrees Celcius first, and why?
Or does the Mpemba Effect say that I don't know until I experiment,
because
the water, mugs, etc all have an effect?
[/quote:0701cb6cab]
How much milk did you add to A?
How much water per cup is there?
Do both cups have the same amount of liquid in them?
Is it skim milk or Whole?
What is the temperature of the Room? |
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| coffee |
| Posted: Wed Jan 26, 2005 4:26 pm |
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Guest
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"relay61:13:214:23" <nospam@nospam.com> wrote in news:35qesnF4phjfaU1
@individual.net:
[quote:8567bfa4fc]
"coffee" <coffee@dnac48.dabsol.co.uk> wrote in message
news:Xns95EAC7CB8C67A28762153tmichanet@ptn-nntp-reader04.plus.net...
[/quote:8567bfa4fc]
[snip]
[quote:8567bfa4fc]Which mug will cool to 60 degrees Celcius first, and why?
Or does the Mpemba Effect say that I don't know until I experiment,
because the water, mugs, etc all have an effect?
How much milk did you add to A?
How much water per cup is there?
Do both cups have the same amount of liquid in them?
Is it skim milk or Whole?
What is the temperature of the Room?
[/quote:8567bfa4fc]
There will be 40 milli litres of milk. It is semi-skimmed milk. In the UK
semi skimmed milk has a legally defined fat content.
Both cups will end up having the same amount of liquid in them, 320 milli
litres.
The room is coldish, 15 degrees celcius.
The cups are not covered. The mugs will be given an equal amount of
stirring with a stainless steel tea spoon. |
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| coffee |
| Posted: Wed Jan 26, 2005 4:28 pm |
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Guest
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"CWatters" <colin.watters@pandoraBOX.be> wrote in
news:dtTJd.5897$AE6.610499@phobos.telenet-ops.be:
[quote:5ca676ef89]"coffee" <coffee@dnac48.dabsol.co.uk> wrote in message
news:Xns95EAC7CB8C67A28762153tmichanet@ptn-nntp-reader04.plus.net...
I have two identical, normal, coffee cups.
I have some milk, at 4 degrees Celcius.
I have some water in a kettle which has just boiled.
I pour a little bit of milk in mug A, and then add water.
I pour water into mug B (no milk).
Which mug will cool to 60 degrees Celcius first, and why?
A: Mug A with milk
In effect you start off with two mugs full of similar liquids but one
is slightly cooler than the other. The cooler one (Mug A) will reach
60 first. Why? Because both mugs cool down at roughly the same rate
and mug A has a "head start".
That all assums a) it's only a little milk and mostly water in A and
b) that the outside temp is < 60C...
[/quote:5ca676ef89]
But your proof would seem to disprove the Mpemba effect; a hot liquid can
freeze before a cool liquid. This is what I'm wondering: when does the hot
liquid "overtake" the cool liquid to be able to freeze first? |
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| CWatters |
| Posted: Wed Jan 26, 2005 5:31 pm |
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Guest
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"coffee" <coffee@dnac48.dabsol.co.uk> wrote in message
news:Xns95EAD943AFD2028762153tmichanet@ptn-nntp-reader04.plus.net...
[quote:15a22c6a08]But your proof would seem to disprove the Mpemba effect; a hot liquid can
freeze before a cool liquid.
[/quote:15a22c6a08]
But you didn't mention freezing. You said 60C. |
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| CWatters |
| Posted: Wed Jan 26, 2005 5:35 pm |
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Guest
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"coffee" <coffee@dnac48.dabsol.co.uk> wrote in message
news:Xns95EAD943AFD2028762153tmichanet@ptn-nntp-reader04.plus.net...
[quote:6025bc3408]But your proof would seem to disprove the Mpemba effect; a hot liquid can
freeze before a cool liquid.
[/quote:6025bc3408]
I believe the word is "can" not "must". It's quite possible for the cold one
to cool down and freeze before the hot one even allowing for the Mpemba
effect. |
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| relay61:13:214:23 |
| Posted: Wed Jan 26, 2005 7:03 pm |
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Guest
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"coffee" <coffee@dnac48.dabsol.co.uk> wrote in message
news:Xns95EAD916B837B28762153tmichanet@ptn-nntp-reader04.plus.net...
[quote:92e78515e4]"relay61:13:214:23" <nospam@nospam.com> wrote in news:35qesnF4phjfaU1
@individual.net:
"coffee" <coffee@dnac48.dabsol.co.uk> wrote in message
news:Xns95EAC7CB8C67A28762153tmichanet@ptn-nntp-reader04.plus.net...
[snip]
Which mug will cool to 60 degrees Celcius first, and why?
Or does the Mpemba Effect say that I don't know until I experiment,
because the water, mugs, etc all have an effect?
How much milk did you add to A?
How much water per cup is there?
Do both cups have the same amount of liquid in them?
Is it skim milk or Whole?
What is the temperature of the Room?
There will be 40 milli litres of milk. It is semi-skimmed milk. In the
UK
semi skimmed milk has a legally defined fat content.
Both cups will end up having the same amount of liquid in them, 320 milli
litres.
The room is coldish, 15 degrees celcius.
The cups are not covered. The mugs will be given an equal amount of
stirring with a stainless steel tea spoon.
[/quote:92e78515e4]
so a wag is Cup A would start at (100C*(320-40)+40*4 ) / 320 or 88 C
and cub B would be at 100 C
Cup A has 18 C to go and Cup B has 40 C to go.
Nice the room is cool, dont have to worry about the approch tail (if room
was 55 C)
Thermal transfer rates are about the same (close in absolute temp for
radiation)
If it took A 10 min to get to 60C, Cup B would take 10*40/18 or 22 min
(remember this is a linear "wag", I think it would be a little shorter)
I side stepped some "details" assuming A would take 10 min to get to 60C |
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