- #1
"pi"mp
- 129
- 1
Homework Statement
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?
Homework Equations
(i) Q=mCT and (ii) Q=mL_f
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!