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'[OT] Sunday science - pondering.'
2011\09\24@203644 by

You pour equal quantities of hot tea into identical cups.

After pouring cold milk into cup A, the phone rings. You chat for two minutes then pour the same quantity of equally cold milk into cup B.

Which cup is now hotter, or are they the same?

(I got this off the ABC website).

Colin
--
cdb,  on 25/09/2011

On Sat, Sep 24, 2011 at 8:36 PM, cdb <colinbtech-online.co.uk> wrote:

> You pour equal quantities of hot tea into identical cups.
>
> After pouring cold milk into cup A, the phone rings. You chat for two
> minutes then pour the same quantity of equally cold milk into cup B.
>
> Which cup is now hotter, or are they the same?
>
> (I got this off the ABC website).
>
> Colin
>

I'll have a stab at it.

Let's make some assumptions here about the integrity of the question itself..

1. The amount of hot tea isn't specified. Hot tea only adds heat to the cup..
Since amount isn't specified, let's assume 0 mols of hot tea.

2. Let's assume the room temperature is 20 degrees, and the "cold" milk is 5
degrees just before being poured.

So pour some 5 degree milk into cup A. Wait two minutes. Assume the
temperature of cup A is now 3 degrees after being exposed to air. Now pour
cold milk into cup B, the temperature of cup B is 5 degrees. So cup A is of
higher temperature than cup B.

> > Which cup is now hotter, or are they the same?

This is Ye British English ande mindsette at work.

Here "cup" refers to the contents of the cup. ie the tea + water +
milk combination. And not to the eg bone china container.

Also, the problem probably assumes that the cup=container has infinite
thermal resistance and zero thermal mass.
ie considering convection and radiation from the top surface probably sufficeth.

Clue: Fluids will transfer energy to their surroundings at an
increasing rate as they are heated relative to their environment.

NB - clue just provides more degrees of freedom to argue over.

It was meant as some light hearted fun, but with serious scientific principles behind it. It is actually intended for school teachers of I assume secondary school kids.

Mind you, you did miss stating the actual 'law' of heat and and less heat, even though of course your last sentence is correct, though I'm less certain about your immediate statement before it.

By the way are you sure that the temperature of cup 'B' will only be 5 degrees?

Colin
--
cdb, colinbtech-online.co.uk on 25/09/2011
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This email is to be considered private if addressed to a named  individual or Personnel Department, and public if addressed to a blog,  forum or news article.
On Sat, Sep 24, 2011 at 9:17 PM, cdb <colinbtech-online.co.uk> wrote:

>
> It was meant as some light hearted fun, but with serious scientific
> principles behind it. It is actually intended for school teachers of I
> assume secondary school kids.
>
> Mind you, you did miss stating the actual 'law' of heat and and less heat,
> even though of course your last sentence is correct, though I'm less
>
> By the way are you sure that the temperature of cup 'B' will only be 5
> degrees?
>

That's exactly the problem with the question. There's too many uncertainties
and variables left out. Initial temperatures aren't provided, etc. But for
its purpose, I don't think it's meant to be complicated
> That's exactly the problem with the question. There's too many uncertainties
> and variables left out. Initial temperatures aren't provided, etc. But for
> its purpose, I don't think it's meant to be complicated.

Hotter fluids cool faster than cooler fluids.
Colour makes a difference to radiation rate and maybe to convection rate.
Effects seem to go in the same direction, but arguments arise over
this among people who think they understand the issues.

Received from cdb at 09/25/11 00:36 UTC:

>You pour equal quantities of hot tea into identical cups.
>
>After pouring cold milk into cup A, the phone rings. You chat for two
>minutes then pour the same quantity of equally cold milk into cup B.
>
>Which cup is now hotter, or are they the same?
>
>(I got this off the ABC website).
>
>Colin
>--
>cdb,  on 25/09/2011

Cup B will be cooler because it was much hotter then B for two additionalminutes and rate of heat loss is a function of temperature difference.  So cup B lost more heat during that 2 minutes than cooler cup A did, so when milk of the same temp as added to cup A was added to B it became cooler than A.  So B is cooler.

Jim H

On 2011-09-24, at 5:36 PM, cdb wrote:

> You pour equal quantities of hot tea into identical cups.
>
> After pouring cold milk into cup A, the phone rings. You chat for two
> minutes then pour the same quantity of equally cold milk into cup B.
>
> Which cup is now hotter, or are they the same?
>
> (I got this off the ABC website).
>
> Colin

Cup A will be hotter.

Newton's law of cooling states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. Cup B, being hotter initially and therefore have a greater heat difference, will transfer more energy (heat) to the surrounding than cup A for a given period. Once the milk is subsequently added, cup B will be cooler.

On Sep 24, 2011, at 8:07 PM, Jim Higgins wrote:

> rate of heat loss is a function of temperature difference.

Also, the milk in cup A essentially gets to warm up for two minutes,  while the milk added to cup B stayed cold (by magic, I guess.)

BillW
It is a trick question as Tea should be added to Milk not Milk to Tea :
::It is a trick question as Tea should be added to Milk not Milk to Tea

Aha, so would we get a different result? :)

Colin
--
cdb, colinbtech-online.co.uk on 25/09/2011
Web presence: http://www.btech-online.co.uk   Hosted by:  http://www.justhost.com.au
This email is to be considered private if addressed to a named  individual or Personnel Department, and public if addressed to a blog,  forum or news article.
> > rate of heat loss is a function of temperature difference.
>
> Also, the milk in cup A essentially gets to warm up for two minutes,
> while the milk added to cup B stayed cold (by magic, I guess.)

Got put back in the fridge while the phone was answered (or whatever the interrupt was)? ;))

-- Scanned by iCritical.
> ::It is a trick question as Tea should be added to Milk not Milk to Tea
>
> Aha, so would we get a different result? :)

You get a different taste. It has been shown scientifically that there are compounds in milk that change differently depending on the rate of temperature change. You get different rates of temperature change in the milk when pouring hot tea into cold milk compared with pouring cold milk into hot tea.. The difference must be small, but it is enough to change the way the compounds in the milk break down.

-- Scanned by iCritical.
It's why the floral design on the cup makes a difference that puzzles me.

Not a true black-body, perhaps
> > ::It is a trick question as Tea should be added to Milk not Milk to Tea
> >
> > Aha, so would we get a different result? :)
>
> You get a different taste. It has been shown scientifically that there are compounds in milk that change differently depending on the rate of temperature change. You get different rates of temperature change in the milk when pouring hot tea into cold milk compared with pouring cold milk into hot tea. The difference must be small, but it is enough to change the way the compounds in the milk break down.

The difference is not overly small.
You don't need science - just a taste test.(which can be "Science" of course).

For say 20cc milk and 250cc black tea.
Say milk at 20C and tea at 95C.
Tmax of tea, white, drinking for the use of = (20 x 20 + 200 x 95)/(20
+ 250) = ~ = 72C
(You can add 273.16 to all temperatures if desired - result is the
same)(or exactly 273.16 higher)

If you add milk to black tea the first in milk is raised to very close
to black tea temperature of 95C.
If you add black tea to milk there will be some raising of milk
temperature but the bulk surrounding milk tends to keep it down.

No absolute temperatures here but lots on protein denaturing
http://food.oregonstate.edu/learn/milk.html

""temperatures above 65° C increase viscosity due to the denaturation
of whey proteins"
and much more
http://www.foodsci.uoguelph.ca/dairyedu/chem.html

Grist
http://www.elmhurst.edu/~chm/vchembook/568denaturation.html

More grist
http://www.milkfacts.info/Milk%20Composition/Protein.htm

OTT hot
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=5161180

Urk
http://pubs.acs.org/doi/abs/10.1021/jf00012a013
> It's why the floral design on the cup makes a difference that puzzles me.
>
> Not a true black-body, perhaps?

Not to mention what species of bone they used in the bone-China.

(You think that's not where it got the name, don't you, don't you ??? :-) )

Q = m.c. delta(t)

On Sun, Sep 25, 2011 at 5:10 PM, RussellMc <apptechnzgmail.com> wrote:
>> It's why the floral design on the cup makes a difference that puzzles me..
>>
>> Not a true black-body, perhaps?
>
> Not to mention what species of bone they used in the bone-China.
>
> (You think that's not where it got the name, don't you, don't you ??? :-) )
>
>
>  R
>
....You think that's not where it got the name, don't you, don't you ???

Received from William \"Chops\" Westfield at 09/25/11 05:17 UTC:

>On Sep 24, 2011, at 8:07 PM, Jim Higgins wrote:
>
> > rate of heat loss is a function of temperature difference.
>
>Also, the milk in cup A essentially gets to warm up for two minutes, while
>the milk added to cup B stayed cold (by magic, I guess.)
>
>BillW

The rate of temperature change will be proportional to the difference between substance temperature and room temperature.

Using typical temperatures...

Cold Milk       2C
Tea Black       90C
Tea Green       75C
Room Temp       25C

Tastes vary as to the amount of milk to add.  (I prefer none.)  Let's assume 25% milk.

Black Tea + Milk        68C
Green Tea + Milk        57C

Delta T vs room temp

Cold Milk       23C

Tea Black       65C
Black Tea + Milk        43C

Tea Green       50C
Green Tea + Milk        32C

Hot tea has a larger delta T vs room temp than the milk or the milk/tea mixture, so it will lose heat faster than the mixtures and the cold milk will absorb heat slower than the hot tea loses heat.

The result is that cup B is cooler after final addition of milk.

Jim H
On 25/09/2011 12:10, alan.b.pearcestfc.ac.uk wrote:
> You get a different taste. It has been shown scientifically that there are compounds in milk that change differently depending on the rate of temperature change. You get different rates of temperature change in the milk when pouring hot tea into cold milk compared with pouring cold milk into hot tea. The difference must be small, but it is enough to change the way the compounds in the milk break down.
>

But tea tastes more of tea with no milk.

Though I always wondered about the Rancid yak butter. Surely the black (red really) or Green Tea would be better on its own?

If mixing hot and cold liquids the sooner you mix the warmer it is I think, as the hotter material looses heat faster assuming a constant thermal resistance.. I'm sure this was in New Scientist many years ago
I'd always assumed buttered tea was a source of calories
in a cold climate.

No yaks handy, but a bit of grocer's butter in hot tea is not
On 25/09/2011 17:02, John Gardner wrote:
> No yaks handy, but a bit of grocer's butter in hot tea is not
You can milk a Grocer?

....

I hope that is like Baby Oil and not like Olive Oi
> You can milk a Grocer?

Certainly. You can fleece old ladies too. And make cup cosies
with it so you never have to worry about cold cha
At 12:02 PM 9/25/2011, you wrote:
>I'd always assumed buttered tea was a source of calories
>in a cold climate.
>
>No yaks handy, but a bit of grocer's butter in hot tea is not

It could also keep the tea hot!

In South-West China (Yunnan province) there's a local dish called "crossing
the bridge noodles*" (guo4 qiao2 mi3 xian4 - literally cross bridge rice noodle)

It has a layer of oil floating on top that prevents evaporation, which is the
major source of heat loss for a hot bowl of noodles ... or tea).

* There's a legend involving a scholar, his wife and her invention to keep
his lunch hot whilst delivering it-- I'm sure Google has the details.

Best regards,

Spehro Pefhany --"it's the network..."            "The Journey is the reward"
speffinterlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com

....It could also keep the tea hot...

Doh!!!

Thanks, Speff - I know that story too. Can't fix dumb, I guess..
> ...You think that's not where it got the name, don't you, don't you ???
>

http://en.wikipedia.org/wiki/Bone_china

Bone china is a type of soft-paste porcelain that is composed of bone
ash, feldspathic material and kaolin. It has been defined as ware with
a translucent body containing a minimum of 30% of phosphate derived
from animal bone and calculated calcium phosphate[1]. Developed by
English potter Josiah Spode, bone china is known for its high levels
of whiteness and translucency[2], and very high mechanical strength
and chip resistance
....
The first development of what would become known as bone china was
made by Thomas Frye at his Bow porcelain factory near Bow in East
London in 1748. His factory was located very close to the cattle
bones. Frye used up to 45% bone ash in his formulation to create what
he called ‘fine porcelain.’ Although in quality it rivalled porcelain
imported from Europe and China the factory was not a commercial
success
....
The production of bone china is similar to porcelain, except more care
is needed because of its lower plasticity and a narrower vitrification
25% Cornish stone and 50% bone ash.[10] The bone ash that is used in
bone china is made from cattle bones that have a lower iron content.
These bones are crushed before being degelatinised and then calcined
at up to 1250°C to produce bone ash[11]. The ash is milled to a fine
particle size[12]. The kaolin component of the body is needed to give
the unfired body plasticity which allows articles to be shaped.[13]
This mixture is then fired at around 1200°C[14]. The raw materials for
bone china are comparatively expensive, and the production is
labour-intensive, which is why bone china maintains a luxury status
and high pricing.

Cattle, they say.

____________

http://www.howstuffworks.com/lenox.htm

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