# Equilibrium Temperature and composition

## Homework Statement

Describe the composition and temperature of the equilibrium mixture after 1.0 kg of ice at -40*C is added to 1.0 kg of water at 5.0*C.

## Homework Equations

$$\begin{gathered} Q = mc\Delta T \hfill \\ Q = mL \hfill \\ \end{gathered}$$

Book answer:1.2kg ice, 0.80 kg water, all at 0*C

## The Attempt at a Solution

I'm not quite sure how to set this one up. I've tried:

$$m_i c_i \Delta T_i + m_w c_w \Delta T_w = 0$$

With this I found the equilibrium temperature to be -9.8*C....

## Answers and Replies

To begin writing down the equations to yield the equilibrium temperature, the first thing one has to do is to determine the phase of matter the equilibrium point.

So, to start, you need to quantitatively compare the amount of heat required to raise the temperature of ice to 0 degC, heat absorbed from the water to decrease the temperature to 0 degC, and the heat required to freeze/melt all the water/ice. At which phase does the heat removed from the water= heat absorbed by the ice?