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/sci/ - Science & Math

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2888126 No.2888126 [Reply] [Original]

I pose this question to you. Assume a cup made of a perfect insulator. There is a large amount of water in the cup such that the ratio of water in contact with the cup to water in contact with the cool air is very large. When will the water cool off the fastest? The height of the cup above the surface of the water is the object of our attention here.

When will the water cool off the fastest? When the height is very large, when the height is basically level with the surface of the water, or at some point in between?

This isn't homework; I already know the answer. In fact, the rigorous answer is pretty hard to work out to the point where even physics grad students wouldn't bother unless it was part of their research. But what do you think?

>> No.2888142
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2888142

What does /sci/ think of Ika Musume?

>> No.2888144

It will cool off faster when closer to cool air and less cup height.

>> No.2888141
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2888141

Zero, because the heat distribution would have less insulated space to traverse before leaving the system.

Math might be hard, but its fucking common sense.

>> No.2888148

cools fastest right at the start; when the cup is full.

>> No.2888152

Yall niggas sayin' zero forget that a larger amount of Hot liquid takes more time to cool.

>> No.2888154

If you're asking us to just guess then my intuitive answer would be when the brim is level with the surface, because it will allow heat to radiate off to the sides faster.

But since you bother to ask this question, i have a sneaking feeling that the right answer is not the intuitive one.

I don't know, i suck at physics.

>> No.2888164
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2888164

Is that an optimization problem

>> No.2888166

>>2888141
While h = 0 is indeed the right answer, it's not because of radiation. Most heat is lost in the evaporation of water. When the water is in the cup, the diffusion of evaporated water to the outside will be hampered, so the concentration of water vapor at the surface is higher, limiting the evaporation rate. The higher the water comes, the less resistance there will be against diffusion and thus the faster the evaporation will be.

>> No.2888167

>>2888152
My interpretation was that the amount of liquid is independent of the height of the container.

Also, is rate of cooling dependent of liquid amount?

>> No.2888172

OP, tell us more about the details. Is that cup a perfect cylinder surface open at the top?

>> No.2888177

>>2888152
Sorry, I should be clear: the VOLUME of water is the same. It's the height of the cup that matters.

As it turns out, though, since the surface area of the air-contacting area is much smaller than the cup-contacting area, it doesn't matter.

This is a question of power, or how much heat leaves per unit time.

>> No.2888186

>>2888172
Yes, the cup is open at the top. It's perfectly round, too, though that doesn't matter.

Even if you can't do the math, if you understand thermodynamics you can figure it out.

>> No.2888190

>>2888167
It depends on heat transfer, difference of temperature (as in 100ºC water/ loses heat to the air{ambient temperature) faster than 50ºC water) and some other stuff

captcha very related
difficult. ratedsty

>> No.2888195

When you spill it on your penis as you hold the cup between your legs in the car.

>> No.2888202

>>2888195
perfect insulating underwear ftw

>> No.2888239

theoretically it should be when the height is zero,

however realistically the height being zero would mean incredible pressure on the liquid meaning it would not cool of because particles could not escape as fast.


you really can't say without more detail. Is it an ideal Liquid? what is it's triple point and when does it become a super critical fluid? What is the temp at which the fluid is held and what is the enviroments temp?

all of these matter...

>> No.2888271

>>2888239
ignorantfag here
Why would the height being zero mean incredible pressure on the liquid?

>> No.2888273

Provided the volume is constant, then the height have to influence to the geometrical shape of the cup/cylinder. Which mean that when the height is very large, spreading the entire fluid volume as thin film on the bottom of the cup, it will cool the fastest due to massive contact area with air.

>> No.2888288

>>2888273
I guess it's a winrar taking into account op didn't provide anything that didn't allow this.

>> No.2888363

>>2888271
You're not ignorant; he's just wrong. It is entirely possible to have a liquid that not only fills the entire volume of the cup, but then some (see: cohesion).

>> No.2888367
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2888367

>>2888363
addendum: this is best expressed via the "water on a penny" experiment

fill an eye dropper with water and release a single drop onto the face of a penny. the water won't spill over and it'll create a bubble due to cohesive forces.

pic related

>> No.2888686

OP here. The answer is (c). While it's obviously not (a), (b) does seem to be the most reasonable answer. However, keep in mind what happens as something cools.

The velocities of the air molecules follows a Boltzmann distribution. If the height is too large, only the very fastest molecules escape and the heat transfer is slow. When it's extremely low, at first a ton of moderately fast molecules will escape. However, what is left behind is a very sharp distribution of slow molecules. They'll spend a lot of energy reaching an equilibrium state with very few molecules fast enough to cool off the liquid.

Instead, at some optimum height, very fast molecules will escape, but the moderately fast molecules will remain to absorb heat. Put another way, if you let out too much heat too fast at the start, you won't have anything to help conduct slower molecules away.

The correct answer is (c).

>> No.2888711

presumably the larger the cup the faster the water will cool, due to the water radiating more heat. im probably very late but to be fair i didnt read up on any of your posts.

>> No.2888718

>>2888686
citation needed

>> No.2888747

>>2888686
I don't know OP. Taking heat out of a 1-molecule-sized layer while you have an infinitely (well not that much) large cup sounds better than what you just said.
However even this can fit at "height is something inbetween" lol