Question in thermodynamics-melting of ice.

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The discussion revolves around a thermodynamics problem involving the mixing of ice and water at different temperatures. The user attempts to calculate the final temperature and the amount of water produced by melting ice, using heat transfer equations. Initial calculations yield temperatures that exceed the expected limits, indicating that not all ice has melted. The user seeks guidance on determining how much ice remains after some has melted, emphasizing the need to balance the heat gained by ice with the heat lost by water. The conversation highlights the importance of understanding phase changes and heat transfer in thermodynamic calculations.
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Homework Statement



Ice of mass 2 kg at -20 degrees C and 5 kg water at 20 degrees C are mixed. Find the net amount of water in the container. (Specific heat of water=1cal/g degrees C, specific heat of Ice = 0.5 cal/g degrees C, latent heat of fusion=80cal/g degrees C)

Homework Equations



Heat lost by water=heat gained by ice
Heat=m.C.(t2-t1)
Where m is mass of substance, C is specific heat of substance, t1 is initial temperature, t2 is final temperature.
Heat=m.L
Where, m is mass of substance, and L is latent heat of substance (latent heat of fusion).



The Attempt at a Solution



Well, the first thing I did is to equate the heat lost by water to the heat gained by the ice. Putting all the variables in the equation,

(2kg)(0.5 cal/g degreesC)(T- (-20 degrees C))=(5kg)(1cal/g degrees C)(T-20 degrees C)
Where, I have assumed T to be the final temperature.

On solving the equation, I'm getting T=30 degrees C which is obviously not possible since, it is higher than the temperature of water.

This probably means that the final temperature is higher than zero.
So I add the latent heat equation.
(2kg)(0.5 cal/g degrees C)(0-(-20)) + (2kg)(80cal/g degrees C)+(2kg)(0.5 cal/g degrees C)(T-0)=(5kg)(1cal/g degrees C)(T-20)
T=70 degrees C (Again, not possible)

I'm assuming this means that all the ice has not melted. But, I have no idea as to how to proceed from this point. Since it is asking the amount of water in the container, some amount of ice has melted and some amount has not melted. How do I ascertain how much ice has melted?
Help will be appreciated.
Thanks.
 
Last edited:
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What gets heated= what gets cooled
Ice will get heated from -20 C to ice at 0 C, the ice at 0 C will get heated, changing to water at 0 C = Water getting cooled from 20 C to water at 0 C

I would find out when ice gets heated from -20 to 0 how much the water gets cooled.
Then I would find out what mass of ice is needed to cool the water from the new temperature to 0 C

Subtract from initial amount of ice to get amount of ice left
 
What gets heated= what gets cooled
Ice will get heated from -20 C to ice at 0 C, the ice at 0 C will get heated, changing to water at 0 C = Water getting cooled from 20 C to water at 0 C

I would find out when ice gets heated from -20 to 0 how much the water gets cooled.
Then I would find out what mass of ice is needed to cool the water from the new temperature to 0 C

Subtract from initial amount of ice to get amount of ice left
 

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