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 A scaled-down experiment (Posted on 2013-04-17)

2.997 kg of ice at -35 degrees Celsius are thoroughly mixed with 138.6 kg of water at 3.9 degrees Celsius in a well-insulated container at standard temperature and pressure.

Determine the proportions of ice (if any) and water in the final mixture.

Bonus: what is being simulated?

 No Solution Yet Submitted by broll No Rating

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 Solution (w/o bonus) | Comment 1 of 2
With specific heat of ice at 2.108 kJ/kg-K (or C), water 4.187 kJ/kg-K, and heat of fusion of 334 kJ/kg

Warming the ice to 0deg C = 2.997*2.108*35=221.118 kJ

Melting the ice @ 0 C to water @ 0C = 2.997*334=1000.998 kJ

Cooling the initially liquid water to 0deg = 138.6*4.187*3.9 =2263.242 kJ

So the ice melts completely.  Going through the algebra, I get a final state of of 141.597 kg of liquid water at 1.758 C

I have no idea what this represents, but a wild guess, based on the 3.9C initial water temperature may have something to do with ice having less density than water at around 4 C?  How this is related to the problem I can't guess.

Edited on April 28, 2013, 10:25 am

Edited on April 28, 2013, 10:26 am

Edited on April 28, 2013, 10:28 am
 Posted by Kenny M on 2013-04-28 10:25:13

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