Calculate temperature of mixed water.

Question

I have two bottles of water. They are 20 oz. containers. One bottle has 12 oz. at 40°F, the other has 6 oz. at 72°F. If I mix the two in one container, what will the resulting temperature be? Please show step-by-step solution.

This is not a homework problem.

Answer 1

The heat added or removed is equal to the specific heat of water times the mass times the change in temperature.

In this case, the heat lost by the 72 °F sample is the same as the gained by the 40 °F sample.  Call X the final temperature.  The specific heat of water remains the same, so

12 oz * (X - 40 °F) = 6 oz * (72 - X °F)

(12 / 6) oz * (X - 40 °F) = (72 - X °F) or 2 oz * (X - 40 °F) = (72 - X °F)

2 X - 80 = 72 - X

3 X - 80 = 72

3 X = 72 + 80 = 152

X = 152 / 3 = 50 2/3 °F  (a little less than 51 degrees)