Question in thermodynamics-melting of ice.

[hale2bopp]

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.

 

[RTW69]

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

 

[RTW69]

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