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Specific & Latent Heat Question

Two lumps of ice, at 0oC, each of mass 20g, are added to a glass containing a mixture of alcohol and water at a temperature of 15oC. The heat capacity of the glass and its contents is 600 J/K. When the system has reached equilibrium how much ice is there?

I'm really not sure how to go about this. Do you assume that since its asking for the amount of ice, the final temperature will be zero? What goes the heat capacity of the contents have to do with it?

Any guidance is much appreciated!
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Avatar for Phichi
Phichi
11
Original post by Bibloski
Two lumps of ice, at 0oC, each of mass 20g, are added to a glass containing a mixture of alcohol and water at a temperature of 15oC. The heat capacity of the glass and its contents is 600 J/K. When the system has reached equilibrium how much ice is there?

I'm really not sure how to go about this. Do you assume that since its asking for the amount of ice, the final temperature will be zero? What goes the heat capacity of the contents have to do with it?

Any guidance is much appreciated!


The mass of the glass and its content is irrelevant, the heat capacity is joules per kelvin, it's mass is already included in that value. When the ice goes into the mixture, the ice beings to warm up, and the mixture begins to cool. However, the ice is at zero degrees Celsius, thus it will being to melt into water. The question is, will all the ice melt before the mixture reaches zero degrees? How much energy in joules will the mixture transfer to the ice before it reaches zero degrees c? Use the latent heat of fusion for water to work out how much energy the ice needs to fully melt. Chances are the mixture will reach zero before all the ice melts, work out the amount of energy the mixture will transfer, and the mass of ice that will melt as a result of that, from there you can calculate the remaining mass of ice trivially.
Reply 2
Avatar for Bibloski
Bibloski
OP
Original post by Phichi
The mass of the glass and its content is irrelevant, the heat capacity is joules per kelvin, it's mass is already included in that value. When the ice goes into the mixture, the ice beings to warm up, and the mixture begins to cool. However, the ice is at zero degrees Celsius, thus it will being to melt into water. The question is, will all the ice melt before the mixture reaches zero degrees? How much energy in joules will the mixture transfer to the ice before it reaches zero degrees c? Use the latent heat of fusion for water to work out how much energy the ice needs to fully melt. Chances are the mixture will reach zero before all the ice melts, work out the amount of energy the mixture will transfer, and the mass of ice that will melt as a result of that, from there you can calculate the remaining mass of ice trivially.


Ok thanks. If I have understood correctly I think I know how to approach this now. If we assume the final temperature of the water is 0oC then we can work out the energy transfer from the water:

Q = mcT = CT (where C is the heat capacity) = 600 x 15 = 9000J

So 9000J are transferred from the water to bring it from 15oC to 0oC. You then divide this by the latent heat of fusion for ice to see how much ice this will melt:

9000/ 334,000 = 0.0269kg = 27g

So there will be 40-27 = 13g of ice left (this is the answer in my book so I assume this is correct working?)

What confuses me is that I assumed the final temperature of the water to be 0oC when in reality it may not have been. So how can this process work because the final temperature may not have been? What happens if the final temperature isn't at zero, how do you then approach it?

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