Heavy science Question?

[Lazy-Ferret]

My wife and I had an interesting conversation this morning, to which neither of us know the answer. I thought a quick look on Google would answer it, but I can't find it on there either...

So here is the question...

Assuming there are no outside losses, the room is thermostatically set at 20c.

I have 2 identical jugs of water each with exactly 1 litre of water in, but one is at 30c, and one is at 10c.

if both jugs are left in the room, which will get to 20c first, the hot or cold one?

Also, along the same lines, if I had 1/2litre at 90c, and poured 1/2litre of 10c water into it, what would be the end temp of the 1litre.

To me, these should be a fairly easy way to work this out, but I can't find it anywhere.

[AlexD333]

I know a guy who knows a guy. Let me get back to you

[johnb5177]

http://en.m.wikipedia.org/wiki/Mpemba_effect

Check this out see if it helps, and this one maybe......

http://sciencefair.math.iit.edu/projects/cooling/

[kitchenman]

As the colorific content of the 30C jug is higher I would assumethe 10C jug would get there first
The higher temp one would have more to lose than the lower one had to gain

[AlexD333]

Ok answer from someone I know with a good scientific background.

"Pretty straight forward for both really.
For the first one. The 30' jug will cool down more rapidly than the 10' jug because it has a greater temperature difference from the room, so the temperatures will converge, BUT. it will never quite catch up with the 10' jug, so the 10' jug will reach room temp first, but only just.

The mixing of the two is simply an average.
(90 + 10) / 2 = 50'C

You can work it out by more complicated means and calculate the amount of energy contained in the two jugs and then work out what temperature that would make 1l of water, but you still get the same answer."

Clever stuff I guess

[kitchenman]

So I woz right

[Lazy-Ferret]

Originally Posted by kitchenman

As the colorific content of the 30C jug is higher I would assume the 10C jug would get there first
The higher temp one would have more to lose than the lower one had to gain

I like your thinking, and it does make sense, but is the opposite to what I thought it would be. I thought it would be either the same amount of time, or the hot would cool quicker...

Originally Posted by AlexD333

Ok answer from someone I know with a good scientific background.

"Pretty straight forward for both really.
For the first one. The 30' jug will cool down more rapidly than the 10' jug because it has a greater temperature difference from the room, so the temperatures will converge, BUT. it will never quite catch up with the 10' jug, so the 10' jug will reach room temp first, but only just.

Not sure if it is how you have written it down, but to me this does not make sense.. One has to loose 10', one needs to find 10', so they are both the same temperature difference to the room.

The second one makes sense, when I used to fill the Fish tank, it would take about 4l of boiling water to bring the 16l of 10' tap water up to 30', which I guess is about right.

I am surprised how hard this is to find the answer too.

[solarman216]

just seen this, and my answer would have been, you always lose heat quicker than gain it so in theory the hotter one would get to 20 first but as they near to the target temperature the hotter one will slow down so I would say they will take almost the same time, Rick