# Homework 13 Number 6

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84-g ice cube at 0°C is placed in 883 g of water at 24°C. What is the final temperature of the mixture?

I know that i can find Q using a given value for latent heat. and i know that Q=mc(delta)T. But I'm not sure how to put the equations together.

asked Nov 15, 2013

## 1 Answer

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The melting ice problem can usually be considered in two steps.

1. First, determine if the ice would all melt. If the latent heat needed to melt the ice is larger than the heat produced through cooling down the water to zero degree, then the ice won't all melt and the final product is ice and water mixture which is at zero degree Celsius.

2. If the latent heat to melt the ice is less that the heat produced through cooling down the water to zero degree Celsius, then all ice will melt and the final product would be water at a temperature between zero degree and the initial water temperature.

If (2) is true, then we can work out the problem in the following process -- first assume all ice melted in to zero degree water and find the heat needed. Then this heat would come from cooling the warm water down certain degrees. Find that temperature. Second, find the final temperature by mixing the cooled warm water and the zero-degree-ice-water. In all processes, heat flow would be in identical quantities for both warm and cold objects -- build your equation around this heat flow and we can solve the problem. For example, the last step would use $$M_{warm}c(T_w-T_f)=M_{ice}c(T_f-0)$$

Here $T_w$ is the temperature of the warm water and $T_f$ is the temperature of the final state of the mixed water. c is the specific heat of water.
answered Nov 15, 2013 by (21,750 points)
I am not sure I understand.. will we be applying latent heat concepts to this problem at all?? If so, how would we approach it? I have plugged in my numbers for the equation above and in variations of that equation and I have yet to receive a correct answer. Thanks