Water Temperature mixing together

[strawberry7]

Homework Statement

When 1 kg of water at 100 C is mixed with 10 Kg of water at 0C, the equilibrium temperature will be:

a) exactly 0 C
b) Exactly 50 C
C) Exactly 100 C
d) slightly above 0 C

I think that the answer is D) sligtly above 0 C, but i don't know why. I'm not sure what formula to use, and I've been lookking all over the web and my textbook.

 

[chaoseverlasting]

When you add 1 kg of water in the liquid phase at 100 C, you can find the heat given out by it when its brought down to T c. That is equal to the heat gained by the 10 kg of water at 0c to come to Tc. Solve for T (final temperature).

 

[strawberry7]

so am i sopposed to use the Q= mc (Change in temperature) formula

so like 1 * 4186 * 100
Q = 418600And then 418600 = 10 *4186 *?
= 41860 * t
418600/41860 = t
t = 10

So it's slightly over 0 C ?

 

[denverdoc]

yea, intuitively you can see this is a weighted average kind of problem,
10 parts at 0, 1 part at 100, so ave for 11=9.09 degrees. Now if the water was ice, different animal as latent heats need to be included.