Physics Question

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Hi all,

So after a few drinks in the pub the discussion segway'd into the usual random and rubbish.

One thing I thought about randomly is this:

If you have a room of 25oC ambient temperature, a glass of water at 10oC and a glass of water at 40oC, will the cold water heat to the ambient temperature at the same rate as the hot water will cool to the ambient temperature?

This assumes that the glasses are in the same hypothetical location in the room, using the same glass and the same liquid.

I dont have a physics / 'science' background so i couldnt really figure out either or neither so was hoping some of the brainier gentlemen on here could help :)

Sam
 
Neither will ever reach room temperature, as the rate of heating/cooling slows the closer to the ambient temperature the liquid gets. They will get very close eventually but they will both remain fractionally above or below room temperature.
 
Given that there is no heat source, other than the temperature difference in the room, the hotter water would cool faster than the cooler water heat up, assuming that the thermal conductivity of the 2 glasses is the same, and that they are the same size.
 
Temperature is the thermodynamic driving force behind heat conduction, so the hot water will cool more quickly than the cold water will heat (as the delta T is different).

For future relevance, a more interesting pub debate is if you add milk whilst the tea is brewing, does the tea cool quicker than if you add milk after brewing (for say, 3 minutes). (the answer is that milk should be added after the teabag is removed - not for temperature reasons, but it tastes better :p)
 
-westy- said:
Given that there is no heat source, other than the temperature difference in the room, the hotter water would cool faster than the cooler water heat up, assuming that the thermal conductivity of the 2 glasses is the same, and that they are the same size.
Click to expand...

This, plus evaporation would reduce the volume of the warmer liquid thus accelerating the cooling of the water.

Might want to google the Mpemba Effect which although not an identical scenario is related and interesting nevertheless.

P.S. it is "segue" btw, unless you really did use those cool electric personal transportation devices to migrate between topics :D
 
DRZ said:
This, plus evaporation would reduce the volume of the warmer liquid thus accelerating the cooling of the water.

Might want to google the Mpemba Effect which although not an identical scenario is related and interesting nevertheless.
Click to expand...

I knew I'd forgotten something :p
 
Dave said:
For future relevance, a more interesting pub debate is if you add milk whilst the tea is brewing, does the tea cool quicker than if you add milk after brewing (for say, 3 minutes). (the answer is that milk should be added after the teabag is removed - not for temperature reasons, but it tastes better :p)
Click to expand...

Is this based on the theory that you scald the milk if you put it in before the boiling water? I can't say I've ever noticed much taste difference but I do tend to add the milk afterwards, there's not a set brewing time though.
 
semi-pro waster said:
Is this based on the theory that you scald the milk if you put it in before the boiling water? I can't say I've ever noticed much taste difference but I do tend to add the milk afterwards, there's not a set brewing time though.
Click to expand...

I think so, although I believe it's probably more of a psychological difference if you are used to it in one way. I've always added milk afterwards too but I did it the other way round last week out of laziness and didn't really notice a difference. Then again, it was Sainsbury's Basics tea :p (which actually is pretty decent unlike the Tesco/ASDA cheapo stuff, but of course isn't as good as the Yorkshire tea that sits in my room!)
 
Dave said:
Temperature is the thermodynamic driving force behind heat conduction, so the hot water will cool more quickly than the cold water will heat (as the delta T is different).
Click to expand...

Wait... isn't delta T the relative difference in temperature? In this case, both being exactly 15K?
 
Also, I don't think evaporation should be taken in to account. This type of question is put across as a hypothetical, generally to be considered in a perfect system where such minor factors are discounted. The loss of volume and it's impact on the volume to surface area ratio would be negligible and not worth considering unless you're going far too far into the question than is really necessary.

I suspect both glasses will undergo the same rate of change of temperature, all other things being equal, and arrive at equilibrium at the same time, but I can't recall the rate of heat transfer formulae so I couldn't say definitively.
 
Deadbeat said:
Also, I don't think evaporation should be taken in to account. This type of question is put across as a hypothetical, generally to be considered in a perfect system where such minor factors are discounted. The loss of volume and it's impact on the volume to surface area ratio would be negligible and not worth considering unless you're going far too far into the question than is really necessary.

I suspect both glasses will undergo the same rate of change of temperature, all other things being equal, and arrive at equilibrium at the same time, but I can't recall the rate of heat transfer formulae so I couldn't say definitively.
Click to expand...

Evaporation is endothermic though and the effects cannot be discounted.
 
DRZ said:
Evaporation is endothermic though and the effects cannot be discounted.
Click to expand...

I think they can. Not least because, as I already mentioned, this sort of hypothetical question is normally presented in a perfect system, but also because the rate of evaporation and its associated dispersal of heat is nigh-on negligible when compared to heat transfer acoss the surface of the glass, even more so when you consider a complementary condensation effect that would occur on a glass of water at 10C in a room of 25C, increasing the heat energy in that glass at a comparative rate. Even taking those minor energy changes into account, we're talking about a difference in energy transfer rate of seconds over the course of a process that stretches over minutes, possibly hours. For pub physics, you really don't need to get so precise.
 
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