What is the final temperature of the mixture?

[FlyDoc]

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

Homework Equations

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?

 

[mfb]

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]

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]

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

 

[rushi123]

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]

Please start a new thread for a new question. In addition, please show your attempts to solve the problem.