1. The problem statement, all variables and given/known data So we are given an insulating container with two compartments between which, heat can flow. In the left one, there exists m_1 of water at temp T_1 and on the right there exists m_2 of ice at temp T_2. What is the final composition and temperature? 2. Relevant equations (i) Q=mCT and (ii) Q=mL_f 3. The attempt at a solution So...I know there are three possibilities: (1) The final composition is all water at temp. above 0 degrees Celcius. I'm okay with this. (2) The final composition is all ice at temp. lower than 0 degrees Celcius. I'm okay with this. (3) The final composition is part water and part ice exactly AT 0 degrees celcius. This is where I'm having issues! Let's assume xm_1 of the water turns to ice and ym_2 of the ice turns to water. Where x and y are dimensionless fractions b/w zero and one. ==> We apply the "relevant equations" above s.t. ALL the water is taken to 0 degrees, ALL the ice is taken to 0 degrees (these are equation (i) above) and then the corresponding fractions change phase by using equation (ii) above. Then we apply energy conservation but we have two unknowns, x and y! I can't for the life of me figure out simple secondary relationship b/w x and y s.t. my method has a solution. Thanks for any help!!