# Calorimetry - Water & Ice Problem

1. Nov 1, 2009

### catspajamas

1. The problem statement, all variables and given/known data

A 10 gram quantity of water at 25 degrees Celsius is poured onto a 400 gram block of ice which is at -10 degrees Celsius. Assume that all the heat is contained within these two objects. Determine the final equilibrium temperature.
Specific heat of water is 4186 J/kgK
Specific heat of ice is 2100 J/kgK
Latent heat of fusion of ice is 334,000 J/kgK

2. Relevant equations

Q = mc$$\Delta$$T
Q = mLf

3. The attempt at a solution

Qwater + Qice = 0

Water cools to 0$$\cdot$$C
Q = mc$$\Delta$$T
Q = (0.010 kg)(4186 J/kgK(0$$\cdot$$ - 25$$\cdot$$C)
Q = -1046.5 J

Water freezes at 0$$\cdot$$C
Q = mLf
Q = (0.010 kg)(334,000 J/kgK)
Q = 3340 J

Water, which is now ice, cools to final temperature Tf
Q = mc$$\Delta$$T
Q = (0.010 kg)(2100 J/kgK)(Tf - 0$$\cdot$$C)
Q = 21(Tf)

Ice heats up to final temperature Tf
Q = mc$$\Delta$$T
Q = (0.400 kg)(2100 J/kgK)(Tf - -10$$\cdot$$C)
Q = 840(Tf) + 8400 J

Putting everything together...
Qwater + Qice = 0
-1046.5 J + 3340 J + 21(Tf) + 840(Tf) + 8400 J = 0
861(Tf) = -10,693.5 J
Tf = -12.4$$\cdot$$C

This can't be the right temperature for Tf because the ice starts at -10 $$\cdot$$C and it's supposed to heat up! (Isn't it?)

If someone could please give me a hint as to what I'm doing wrong, I would greatly appreciate it.

Thank you!

2. Nov 2, 2009

### alphysicist

Hi catspajamas,

I have not checked all of your numbers, but this does not look right to me. Notice in the previous quantity, Q is negative when heat leaves the water (as it cools to zero degrees). If water is freezing, is heat entering or leaving the water?