# The Naked Scientists Forum

### Author Topic: Which Cup Cools Down Quicker ?  (Read 2487 times)

#### neilep

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##### Which Cup Cools Down Quicker ?
« on: 08/07/2008 20:21:23 »
Dear Cupologists and Bra Wearers !

Cups are my all time favourite thing for filling with liquid and then drinking from !
Glasses are nice too...but I prefer a cup..or a mug actually.....but not a horse trough !....those are reserved for my annual bath !

See these two photos of two cups ?

and then this one ?

Nice eh ?

Notice the shape of the cups ?....say the water within was very hot...boiling in fact !

Would there be a difference at the speed at which both cups of water cooled down ?

I wish I knew !!...Oh woe is me...how I wish I knew !! [:-[]

End my woe
Let me know !!

*le thanks*

Neil
Cup Handler

mwah mwah mwah mwah

xxxxxxxxxxxxxxxxxxxxxx

#### RD

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##### Which Cup Cools Down Quicker ?
« Reply #1 on: 08/07/2008 21:01:21 »
The cup with the greater  volume of water will take longer to cool, as its surface-area to volume ratio is lower,
(“area” includes the area in contact with the cup).

If you have a thermometer you could perform this experiment and find out which cools faster,
e.g. time how long each takes to cool from 90C to 60C.

Yes I did notice that the cup diameter increases slightly towards the top,
So the water in the fuller cup will have slightly larger area exposed to the air ,
But this is negligible compared with the additional thermal inertia of the larger volume of water.

#### blakestyger

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##### Which Cup Cools Down Quicker ?
« Reply #2 on: 09/07/2008 12:37:18 »
In Newton's Law of Cooling the heat change (ΔQ) is proportional to the mass (m) so it looks as if the larger will cool slower.

#### neilep

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##### Which Cup Cools Down Quicker ?
« Reply #3 on: 09/07/2008 14:21:30 »
The cup with the greater  volume of water will take longer to cool, as its surface-area to volume ratio is lower,
(“area” includes the area in contact with the cup).

If you have a thermometer you could perform this experiment and find out which cools faster,
e.g. time how long each takes to cool from 90C to 60C.

Yes I did notice that the cup diameter increases slightly towards the top,
So the water in the fuller cup will have slightly larger area exposed to the air ,
But this is negligible compared with the additional thermal inertia of the larger volume of water.

Thank You RD

Yes, I was thinking that the fuller cup might actually cool down quicker because of the very reason you mention. But, your explanation helps me understand why not...ta.

#### neilep

• Withdrawnmist
• Naked Science Forum GOD!
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##### Which Cup Cools Down Quicker ?
« Reply #4 on: 09/07/2008 14:22:28 »
In Newton's Law of Cooling the heat change (ΔQ) is proportional to the mass (m) so it looks as if the larger will cool slower.

Thank You blakestyger

Cheers

#### The Naked Scientists Forum

##### Which Cup Cools Down Quicker ?
« Reply #4 on: 09/07/2008 14:22:28 »