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JSHarris - 10,000 Posts And Counting ...


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#21 jsharris

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Posted 03 February 2016 - 09:19 AM

View Postgravelld, on 03 February 2016 - 09:08 AM, said:

Erm, don't feel like you have to explain in detail, a link would do, but wouldn't the temperatures converge assuming the milk goes in the other cup eventually? Surely it just depends when you measure the temperature? I'm visualising a graph of temp v time. Milk-first has a sudden drop when milk is added then lower heat loss rate because of the lower delta. Milk-last starts higher but then has a higher heat loss rate. Eventually I thought they'd curve to meet each other. So doesn't it depend when the tea is tasted and what temperature you can bear it at? What I can't envisage is the milk-last cup to "overtake" the milk-first, even though it has a higher heat loss rate, because it is starting at a higher temp.

The key bit is that the rate of heat loss (which is really the rate at which energy flows out of the tea in the cup) depends on the temperature difference between the tea and the surrounding air, the thermal conductivity of the cup and the surface it's resting on.

There is a fixed quantity of heat energy in each cup at the start, as they each have the same volume of tea at the same temperature. If milk is added first, then when the tea is added the initial temperature of that cup will be lower, because it will mix with the cool milk. If milk is added later than the initial temperature will be higher, until the time where the milk is added.

This means that in that initial period the cup with no milk will lose a lot more heat energy up to the point where the milk is added. From then on it's rate of heat energy loss drops, because the temperature differential has reduced. The cup that already had the milk in will start at a lower initial temperature so will not suffer that additional higher initial energy loss rate.

The cooling curve was measured by Newton (and is referred to as Newton's Law of Cooling) and you can see more detail on it here: https://en.wikipedia..._law_of_cooling

#22 ProDave

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Posted 03 February 2016 - 09:26 AM

The tea cooling argument can be further reinforced:

Black tea (without milk) is black in colour. A Black body radiates heat much faster.

Once the tea has milk added, it's a much more white colour, so quite apart from the lower heat loss due to the lower temperature, it will radiate less heat as well.

By the time you have finished explaining this, said cup of tea will probably have been poured over your head and SWBBO will have stormed off, probably muttering "ignorant ba$tard"

Proving a woman wrong, without starting an argument is a skill I have yet to learn.

Edited by ProDave, 03 February 2016 - 09:30 AM.


#23 SteamyTea

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Posted 03 February 2016 - 09:36 AM

I drink a lot of tea, and I like it strong, with plenty of milk (this is not the same as weak with milk, it is the flavour, not the colour, that is important) and not too hot.
I also use a teabag in a mug, rather than a pot.
So I add the water first, beat the bag, remove the bag and then add milk.
This is more to do with practicality than temperature.

Newton's Law of Cooling is not a straight line, it follows a exponential decay and uses the 'magic' number e, which appears in natural systems all the time (population growth being a good example, energy storage in capacitors, rate of plant growth, wind speed distribution, it is just everywhere).
The key point of Newton's Law of Cooling is that it is proportional to temperature difference and surface area.
This is why a really hot, small house (or animal) looses a disproportionate amount of energy compared to a larger one.

Edited by joiner, 03 February 2016 - 11:40 AM.
added "al" to "proportion" to make "proportional"


#24 gravelld

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Posted 03 February 2016 - 09:41 AM

View Postjsharris, on 03 February 2016 - 09:19 AM, said:

The key bit is that the rate of heat loss (which is really the rate at which energy flows out of the tea in the cup) depends on the temperature difference between the tea and the surrounding air, the thermal conductivity of the cup and the surface it's resting on.
Agree.

View Postjsharris, on 03 February 2016 - 09:19 AM, said:

There is a fixed quantity of heat energy in each cup at the start, as they each have the same volume of tea at the same temperature. If milk is added first, then when the tea is added the initial temperature of that cup will be lower, because it will mix with the cool milk. If milk is added later than the initial temperature will be higher, until the time where the milk is added.
But as *both* of the cups cool, both lines get progressively shallower. The one that was initially hotter with a higher heat loss and temp delta also gets shallower quicker as its delta reduces. This is what I can't get my head around - I thought they would both meet eventually, so it was more of a matter of timing?

One variable I'm not sure about is volume. The milk+tea cup will have more volume I assume, until tea+milk's milk is added.

#25 jsharris

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Posted 03 February 2016 - 09:43 AM

View PostProDave, on 03 February 2016 - 09:26 AM, said:

The tea cooling argument can be further reinforced:

Black tea (without milk) is black in colour. A Black body radiates heat much faster.

Once the tea has milk added, it's a much more white colour, so quite apart from the lower heat loss due to the lower temperature, it will radiate less heat as well.

By the time you have finished explaining this, said cup of tea will probably have been poured over your head and SWBBO will have stormed off, probably muttering "ignorant ba$tard"

Proving a woman wrong, without starting an argument is a skill I have yet to learn.

You could do an experiment to see how big an effect this is. Get two cups of tea, one with milk, one black and heat them so they are at the same temperature (measured with a thermometer) and then check the temperature of each with an IR thermometer, pointing at the surface. The one with the higher reading would have the greater emissivity. It may well be the black tea, but I'd not be surprised if they were both similar, or the white tea had the greatest emissivity. Be interesting to find out.

#26 jsharris

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Posted 03 February 2016 - 09:46 AM

View Postgravelld, on 03 February 2016 - 09:41 AM, said:

Agree.

But as *both* of the cups cool, both lines get progressively shallower. The one that was initially hotter with a higher heat loss and temp delta also gets shallower quicker as its delta reduces. This is what I can't get my head around - I thought they would both meet eventually, so it was more of a matter of timing?

One variable I'm not sure about is volume. The milk+tea cup will have more volume I assume, until tea+milk's milk is added.

Because it's an exponential decay then both cups will tend towards room temperature eventually. The key point was really about the time it takes to cool to a point where the tea would still be considered warm enough to drink, and I chose 15 minutes as a reasonable length of time (my other half would disagree, as she likes to drink tea when it's hot, whereas I'm happy with it being lukewarm)/

Edited by jsharris, 03 February 2016 - 09:47 AM.


#27 gravelld

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Posted 03 February 2016 - 09:52 AM

Right but if milk+tea starts off lower, and the exponential decay means the heat loss for both cups decreases, doesn't that mean tea+milk will stay hotter for longer simply because it started higher, unless you happen to like your tea at room temperature in which case they will be the same.

Also there's the tea+milk cooling overshoot to consider. Recall Cameron from Brussels, this needs sorting out.

p.s. this is me being insatiable ;-)

#28 Alphonsox

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Posted 03 February 2016 - 10:10 AM

I think stopping at room temperature is a cop out, you really need to continue to freezing. I have yet to see a good paper on the effects of tea/milk mix timing on the Mpemba effect. The one that was originally hotter should in theory freeze first.

(and many thanks for the last 10K posts)

#29 declan52

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Posted 03 February 2016 - 10:11 AM

And there you have it in a nutshell. Start of the post congratulating Jeremy on reaching 10,000 and being probably one of the most open honest and knowledgeable guys I have ever had the pleasure of communicating with to discussing the heat loss differences between two cups of tea. Where else would you get it!!!

#30 stones

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Posted 03 February 2016 - 10:14 AM

I remember my introduction to serious tea drinking. Four of us on a shift, 10 teabags in the teapot and allowed to brew for 15 minutes, no more, no less. Came out like tar and still too hot to drink.

Jeremy, congratulations on breaking the 10K barrier.

#31 ferdinand

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Posted 03 February 2016 - 10:16 AM

View Postgravelld, on 03 February 2016 - 09:41 AM, said:

Agree.

But as *both* of the cups cool, both lines get progressively shallower. The one that was initially hotter with a higher heat loss and temp delta also gets shallower quicker as its delta reduces. This is what I can't get my head around - I thought they would both meet eventually, so it was more of a matter of timing?

One variable I'm not sure about is volume. The milk+tea cup will have more volume I assume, until tea+milk's milk is added.

Another variable is that the charge of milk (at what temperature?) has a different (?) effect on a half-cooled cup of tea to a hot cup of tea.

And the tea-drinker can adjust the amount of milk if thay add it themselves later to ensure that it *is* hotter :-), and their life is not controlled by Mrs Bucket the teamaker.

Posted Image

Source:
http://www.thenakeds...xp/-0c2ee7e805/

And congratulations to Jeremy.

But this morning I seem to have mislaid my Zebra burgers to go with my poached egg :-( .

Ferdinand

Edited by ferdinand, 03 February 2016 - 10:36 AM.


#32 gravelld

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Posted 03 February 2016 - 10:30 AM

That illustrates what I was thinking.

There's the dreaded overshoot, at about 16.5 minutes! :D

What is the ideal temperature of a cup of tea anyway?

#33 jsharris

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Posted 03 February 2016 - 10:39 AM

The difference with my experiment was that I added the milk after two minutes for the "add milk later" cup, so that step drop you see in that plot just after the milk was added happens earlier. Other than that, the plots look similar to mine, just offset on the time axis by about ten minutes or so.

#34 gravelld

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Posted 03 February 2016 - 11:23 AM

Gotcha.

#35 SteamyTea

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Posted 03 February 2016 - 11:29 AM

What would be even more fun is to make the tea, add the milk to one of them, then move the mugs to outside before adding the milk to the second mug.
Then you get a partial differential equation. They are much more fun.

#36 NSS

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Posted 03 February 2016 - 04:01 PM

*
POPULAR

I prefer coffee.

#37 notnickclegg

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Posted 03 February 2016 - 04:12 PM

View PostNSS, on 03 February 2016 - 04:01 PM, said:

I prefer coffee.

Finally someone brings some sense into this part of the thread!

Jack

#38 Nickfromwales

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Posted 03 February 2016 - 04:23 PM

Can I kill myself now ?
:blink:

#39 ConstructionChannel

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Posted 03 February 2016 - 04:39 PM

View PostNickfromwales, on 03 February 2016 - 04:23 PM, said:

Can I kill myself now ?
:blink:

NO you've got another 2750 posts before you're even allowed to consider it :P

Edited by ConstructionChannel, 03 February 2016 - 04:40 PM.


#40 recoveringacademic

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Posted 03 February 2016 - 04:49 PM

View PostNickfromwales, on 03 February 2016 - 04:23 PM, said:

Can I kill myself now ?
:blink:

Many Welshmen try every Saturday, down at the Arms Park and various muddy fields all over Wales. Just pop your boots on - you know you can do it.

(Don't)