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Old Mar 6th 2017, 08:15 AM   #1
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Join Date: Mar 2017
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Needs help with my homework

5 liters of water at 70˚c need to cooled to 50˚c.
Specific heat capasity of water is 4200J/kgK
Latent of heat of fusion of water is 3.34 x 10e5 J/kg
and the water density is 2000kg/m3

Q1

Determine the heat lost by the water when ice is added as the water cools to 50˚c

Ans = 420 KJ

Q2

Determine the heat required to melt the ice and raise the temp to 50˚c

Q2 = Heat needed to melt the ice and raise the temperature to 50˚C

Ans = 5.44 x 10e5m J

Q3

Determine the amount of ice to be added to the water to cools it from 70˚c to 50˚c

Since there is no heat loss to the environment, it can be concluded that
Q1=Q2
Ans = 0.772 kg


Q4 >

The question asked, if the heat to the environment is not neglected, what is the relation between the diameter of the mug and the amount of ice needed to cools 7 liters of water from 70˚c to 50˚c.

I'm stuck, I know that the relation is time, needed to cools it naturally and by adding ice but I can't find any formula to relates time in it.

Thanks in advance
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Old Mar 7th 2017, 12:41 PM   #2
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Needs help with my homework

This is a very complicated question as the specifics will depend on many different factors. However, it is possible to make some predictions on the relationship if some assumptions are made. Firstly that the sides are perfectly insulated and second that the rate of heat transfer (whatever that might be, due to conduction and evaporation) is related i.e. proportional to the open surface area of the mug. Since the diameter of the mug is related to the square root of the surface area, the amount of heat lost in a given situation (time, humidity etc.) will be proportional to the square of the diameter of the mug.

The formula will be x - K*D^2 for the amount of ice required if heat lost to the environment is not ignored.

Where K is a constant of proportionality and D is the diameter of the mug. X is the mass of ice required if heat is not lost to the environment.

Note that the actual formula for K is likely to be extremely complicated and likely can only be confirmed by experiment.

The density of water is 1000 kg/m^3
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