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Cooling hot water by adding in cool water and draining out the hot water - Formulae

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Etude
#1
Feb6-12, 02:40 AM
P: 28
Hi!

So this is the scenario.

I have 27 litres of water at 100 degrees Celsius. I have to cool the water to 20 degrees Celsius within 5 minutes. Since the heater power required is too high, I thought this could be done by adding in water at 20 degrees Celsius while draining out the water at 100 degrees Celsius simultaneously. I need to decide on the following: flow rate of cool water in, flow rate of hot water out while making sure the water cools to 20 degrees within the 5 minutes.
I have no idea which formulae can help me out here. Can anyone please advise which formulae can be used?
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sophiecentaur
#2
Feb6-12, 04:58 AM
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Try googling "method of mixtures" to see the sort of approach you need. Basically, it works on the principle of Heat at start = Heat at finish.
Equate the two and you should get an equation with one unknown (if the question has been set correctly).

Total Masses at start times SH times temp drops plus heat added = Total masses at end times SH times temp rises
Think it through and then put in the appropriate values.
Initially, you'd do the sums ignoring heat loss to the surroundings, of course.
Etude
#3
Feb6-12, 06:17 PM
P: 28
Thanx!
I am aware of those formulae but I do not know how to factor in the time restraint and would like some help there.
Will still tinkle around with those formulae till then!

Etude
#4
Feb6-12, 06:44 PM
P: 28
Cooling hot water by adding in cool water and draining out the hot water - Formulae

Oh and it s not a 'question' to be solved as such. More like a design project. So lots of unknowns present.
sophiecentaur
#5
Feb7-12, 06:04 AM
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The approach would be to consider the energy transfers in, say, one minute. You are adding so much water in that minute and the heater is supplying so much energy in that time etc. etc. so you are back to a 'static' situation with an initial state and a final state which will give you the rate of heating per minute (for instance).
Does that help? Often, it can be really useful to do this sort of thing on a spreadsheet, in steps of a minute (or whatever's suitable) and then you can plot a graph of temperature rises as time progresses. (Let the computer take the maths load off your shoulders)

I remember doing the Callendar and Barnes experiment, back in about 1961, at School, with tap water flowing through a heated tube, measuring rate of flow by filling beakers and then reading two thermometers for getting the temperature rise. Happy daze.
Etude
#6
Feb7-12, 05:55 PM
P: 28
OH!!! Ok ! That does help! Basically, the final state at minute none will become the initial state for minute two and so on, right ? Thanx!


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