Temperature change experiment request

[ryanbrit]

As a patriotic British citizen, I am accustomed to waking up and making a cup of tea every morning. I like to drink mine at around 50 degrees Celsius. As I pour my boiling water (100 degrees Celsius) from the kettle into my cup, I always ask the same question...

 

'Would it reach my optimum drinking temperature (50 degrees Celsius) faster if I pour the milk (2 degrees Celsius) into my cup right after pouring the water, or would it reach it faster if I leave the water until it has cooled a little from the ambient temperature and then add the milk?'

 

I guess it is a question of whether an instant mix of cold liquid into a hot liquid will bring a temperature down quicker than a delayed mix of cold liquid into a slightly cooled liquid, with both starting temperatures at 100 degrees Celsius.

 

I am asking if there is someone who can test this, and let me know if there is a difference in time for the temperature to reach 50 degrees in a controlled environment.

 

I am by no means a scientist, this is simply a wonder I have had every morning for most of my life.

 

Have fun & be safe!

[John Cuthber]

It's complicated.

Do you have two cups, a thermometer and a watch? It might be easiest to do the experiment

[studiot]

The milk will cool the mixture by a fixed number of degrees, whatever temperature you add it in at.

The longer you delay adding the milk the more quickly the hot water will cool. (This is known as Newton's Law of Cooling).

In any case you need to leave the bag in unmilked water for a period to infuse as properly as it possibly can in a cup.

[John Cuthber]

Except that it's actually complicated.

 

For a start, Newtons law of cooling also says that the hate of loss of heat is proportional to the hot area.

And if you put more milk in the cup, you increase the depth of tea- and thus the heated area available for heat loss.

 

But, of course the cup above the liquid level would have been heated to some extent anyway- by conduction- but now it's being heated from a heat source at a lower temperature.

Of course, because the cup is quite warm you will get convection effects too. Giving a larger surface - by having a deeper liquid level in the cup- will increase the "chimney" effect ant thus improve cooling.

And of course, some of the heat is lost via the base of the cup- that's probably more nearly constant and depends on the thermal properties- specifically the thermal conductivity and thermal diffusivity of the table (or whatever).

 

If the tea was really hot (it won't be, but just to make the general point) the losses by radiation would be significant- and in that case the temperature of the liquid surface and the nature of that surface would matter. A whiter surface is a poorer radiator of heat (it has to be because it's a poorer absorber- that's Kirchoff's law

Not this one

https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws

this one

https://en.wikipedia.org/wiki/Kirchhoff%27s_law_of_thermal_radiation

 

)

 

 

And then there's the fact that the fat in the milk will rise to the top and reduce evaporative losses- which might or might not be significant - depending on things like the relative humidity, the ambient temperature, the shape of the cup, local wind-speed and so on.

 

Of course, if the milk is frothy- and it will usually have some effect on surface tension- it might act as an insulating blanket on the top of the tea and keep it warmer.

 

Like I said- it's probably easier to get two cups, a thermometer and a stopwatch.

[studiot]

John,why you are making this uneccessarily difficult?

 

My experiments over several years conducted (pun intended) for oither reasons confirm that Newton's law is the dominant factor in this situatiion.

Further I confirm that if you wrap a cloth soaked in cold water round the vessel it will dramatically increase the rate of cooling.

 

Please note also that this is a standard high school physics experiment.

Edited June 5, 2016 by studiot

[John Cuthber]

John,why you are making this uneccessarily difficult?

 

My experiments over several years conducted (pun intended) for oither reasons confirm that Newton's law is the dominant factor in this situatiion.

Further I confirm that if you wrap a cloth soaked in cold water round the vessel it will dramatically increase the rate of cooling.

 

Please note also that this is a standard high school physics experiment.

Why are you making it unnecessarily (two ns and only one c by the way) simple?

 

For example your assertion that "The milk will cool the mixture by a fixed number of degrees, whatever temperature you add it in at."

Implies that the heat capacity of the milk is not temperature dependent- that's not correct.

https://syeilendrapramuditya.wordpress.com/2011/08/20/water-thermodynamic-properties/

 

​Anyway, the big effect - loss of heat from the walls- is balanced by having more hot wall to lose heat from.

Re. "Please note also that this is a standard high school physics experiment."

Shocking as you might find this, I was once a high school student- so I know that.

Why did you post it?

Edited June 5, 2016 by John Cuthber

[Endy0816]

Think he mentioned it in case this was homework related.

 

I don't think I even saw tea in high school :¥

[studiot]

John, thank you for correcting my spelling, I will offer you the same courtesy one day.

 

You called for an experiment.

 

I quoted a series.

 

But you ignored it.

 

I stated there was a dominant factor.

 

You offered effects that can only make small differences to the cooling times, because they are not dominant.

The rate of cooling for the hotter liquid will be greater,

Do you deny this?

 

I also quoted a method of increasing the rate of cooling of either liquid, which has nothing to do with the fringe effects you mentioned.