# What is the final temperature of the mixture?

## Homework Statement

10 g of water from a water ice mixture (0 degrees C) is added to100 g of water at 20 degrees celsius. what is the final temperature of the mixture? C of water =1 kcal/kg*C Latent Heat of Fusion of water=79.7 kcal/kg

Q=mC(Tf-Ti)
Q=mL

## The Attempt at a Solution

I ignored Latent heat of fusion since the 0 degree water form the water-ice is already melted. I just set mC(Tf-Ti) of water from water-ice equal to mC(Tf-Ti) of water. I got 22 degrees. Book answer is 18.2. Where am I going wrong?

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mfb
Mentor

Probably a sign error: One part heats up, one part cools down, so you have to swap the sign on one side. Otherwise, you add the same amount of heat to both parts.

SteamKing
Staff Emeritus
Homework Helper

If you mix water at 0C with some other water at 20C, then the final temp of the mixture must be between 0C and 20C.

ehild
Homework Helper

## The Attempt at a Solution

I ignored Latent heat of fusion since the 0 degree water form the water-ice is already melted. I just set mC(Tf-Ti) of water from water-ice equal to mC(Tf-Ti) of water. I got 22 degrees. Book answer is 18.2. Where am I going wrong?
mC(Tf-Ti) for water and for ice are of equal magnitude but of opposite signs, as the warm water loses heat while the cold water gains.
The sum of the mC(Tf-Ti) terms is zero.

ehild

when 260g of metal shots at 200^C are mixed in an ice-water bath (m of ice is 50g, m of water is 90g) which is in a 105 g copper container, the final temperature of the mixture was 10^C. assuming no heat energy was lost from the system, what is the value of the specific heat capacity of the metal

mfb
Mentor