Thermal Dynamics question for you techno science folk

The important thing is the temperature difference, as heat transfer is proportional to it. Higher the temp difference, faster the heat transfer. Hotter water will transfer heat to the room faster, so by not adding the cooler water to the beaker of hot water it will lose more heat to the room by itself. Add the cool water in at the last minute. Option b).
 
you're mixing up some principles there.

t^4 is stefan-boltzmann for black body radiation. It is not affected by local temperature.

and "4th power of temp difference" is (t1 - t2)^4, not what you wrote.

Whoops, I should probably burn my bachelors degree now. Not done thermo for a few years in my defence.
 
The important thing is the temperature difference, as heat transfer is proportional to it. Higher the temp difference, faster the heat transfer. Hotter water will transfer heat to the room faster, so by not adding the cooler water to the beaker of hot water it will lose more heat to the room by itself. Add the cool water in at the last minute. Option b).

I don't get why people think this logically makes sense.

logically, all you can say is:

"Higher the temp difference, faster the heat transfer. Hotter water will transfer heat to the room faster, so by not adding the cooler water to the beaker of hot water it will lose more heat to the room by itself. BUT it starts from a higher temperature than when we add the cooler water at the beginning. Therefore we need to carefully consider both options"

stuff it, i'll write up the proof....

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http://img140.imagevenue.com/img.php?image=17632_gif_122_581lo.jpg

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http://img168.imagevenue.com/img.php?image=17633_gif2_122_1062lo.jpg
 
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I don't get why people think this logically makes sense.
Probably because that's what they taught me in first year thermodynamics? :p

I'm not going to pretend to understand your maths. I last did that stuff over 12 years ago and yours is undoubtedly correct because this is an internet forum. I'll take your word for it but I won't understand why :p
 
yeah, I delibrately ignored that :p The equation I used is only valid for constant surface area.

You've also assumed that t=t* on your algebra, as you have combined one term in t* with another in t. You're essentially assuming that your heat loss "constant" (/fudge factor) is the same in each case. The last couple of lines of algebra are a little dodgy too - you've taken out a factor of the masses, but it's not been divided through the equation properly by the looks of things?
 
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You've also assumed that t=t* on your algebra, as you have combined one term in t* with another in t. You're essentially assuming that your heat loss "constant" (/fudge factor) is the same in each case.

sorry, all t should be t*, where t* is 10 minutes. the constant is the same, except for the already mentioned case of changing surface area.

and considering that mixing the water can only increase the surface area, which in turn will increase the rate of temperature loss, it can only mean that mixing earlier will result in a lower temperature than mixing later.

e: thats not quite right, it depends on the ratio of volume change to surface area change.
 
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and considering that mixing the water can only increase the surface area,.

Do we know anything of the properties of the larger beaker? Are the sides parallel or is the top of it wider than the bottom. If the sides are parallel then the surface area does not change.

Basically rtfq ;-)
 
Do we know anything of the properties of the larger beaker? Are the sides parallel or is the top of it wider than the bottom. If the sides are parallel then the surface area does not change.

Basically rtfq ;-)

ok, if we take the beaker to be at the environment temperature, and all sides (ok not the bottom :rolleyes:) to be parallel to mavity etc, then surface area is constant, volume increases, and now mixing earlier will keep it hotter than mixing later.
 
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