A mass m of ice at 0 deg C is mixed with a mass 2m of water at 100 deg C in a thermally insulated container. What is the final temperature of the mixture? (Use: specific heat of water = 1 cal/(g*deg C), latent heat of fusion of ice = 80 cal/g.)

10 deg C
100/3 deg C
40 deg C
none of these

Correct answer: none of these

Solution

All the ice melts because the water releases more than enough heat. After melting, the remaining heat (200m - 80m = 120m cal) raises the combined mass 3m of water, giving a final temperature of 120m/(3m*1) = 40 deg C. So the answer is 40 deg C.

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