Re: rate of cooling

On Mon, 21 Jan 2008, vortexsbkny@xxxxxxxxx wrote:

On Jan 21, 1:13 pm, Edward Green <spamspamsp...@xxxxxxxxxxx> wrote:
On Jan 21, 11:55 am, vortexsb...@xxxxxxxxx wrote:

ie. have two water bowls at 100F, with 1lb and 2lb of water each.
What cools down faster? seems like a smaller one, why?

The larger one, since, in the absence of specification to the
contrary, we may assume the small bowl is roughly spherical in shape
and made of a rigid foam insulator with a very small mouth, held in a
room at 100% relatively humidity at 99 F, whereas the larger one may
be reasonably assumed to be over 11' in diamter, and less than 1/2"
deep, being cooled evaporatively by a fan moving not less than 200 cfm
of dry air at STP over the surface.

Those seem like perfectly obvious and inevitable assumptions to me,
and if the author intended otherwise, he might have... excuse me "she"
might have said so.

Thanks for the answer. Actually, I was not using any textbook.
Question is completely made up and came to me during breakfast.
I noticed that my tea was getting colder faster the more I drank of
it.
In other words, liquid held heat less efficiently then when cup was
full.

gotta be a simple physical explanation,
like specific heat capacity related to mass or volume?

No, but heat loss by evaporation is proportional to the surface area of tea open to the air. This is constant (at least approximately - the height of the cup sides above the surface will affect it). The "extra heat" content is proportional to both the volume and the "extra temperature". At 10 shovel-fulls per minute, what can you move faster - a small pile of sand, or a large pile of sand.

You might want to read about the energy requirements of large vs small warm-blooded animals. The ratio of surface area to volume is very important. More or less, the surface area of an animal is proportional to its (length or height) squared, and the volume to it cubed. Heat loss is proportional to area, production of heat is proportional to volume. The large animal has it easier, to the point where it may have trouble keeping cool enough.

With the teacup, similar principles apply (but you're talking about stored heat, not heat production). Note that the effective surface area doesn't change that much - the tea heats the cup, and the surface area of the cup stays constant, regardless of how much tea is in it.

Here is an experiment you can try. Get seven identical teacups or mugs. Fill them all at the same time with hot water.

(a) leave one on the bench
(b) cover one with an upside-down mixing bowl
(c) wrap the sides of one with a few layers of paper, maybe even put a layer of bubble wrap on the outside
(d) cover the top of one with plastic wrap
(e) cover the sides of one with aluminium foil
(f) sit one in a bowl/basin/sink of cold water
(g) sit one on a metal table/sink/plate (or, if you have a metal benchtop, sit one on a cork coaster or suchlike)

Leave for a while, then compare temperatures. The standard introductory fare on heat transfer is: conduction, convection, radiation. You can add evaporation to that too (which involves mass transfer too, so is beyond the simple mechanisms). (b)-(g) are designed to affect these mechanisms of heat transfer. You might also like to try some different combinations of them.

Ideally, try to identify how (b)-(g) affects the different methods of heat transfer. Predict which would have the largest effect. Do the experiment. Were there any surprises?

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

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