Calculate Equilibrium Temperature

[McDonell]

Homework Statement

A 1kg of ice at -30° C is added to 10 kg of steam at 500°C. answer the following questions: a) What is the final phase of the system of ice + steam if no heat escaped from it.
b) What is the final temperature when the equilibrium is established

Homework Equations

Q= mc (delta) T
Q= mL

The Attempt at a Solution

I am assuming that the final phase will be steam.

I have tried multiple times, but I cannot seem to get the answer. I know that

Q(-30 --> 0) + Q (ice fusion) + Q(0 --> 100) + Q(heat of vaporization) + Q(Tf - 100) = Q(Tf - 500).

Any help would be greatly appreciated

 

[gneill]

Why don't you start by showing your calculated values for the various heats that you know (the individual terms of the expression you wrote).

 

[Simon Bridge]

I am assuming that the final phase will be steam.

What is your reasoning for this?
(May be a fair bet for the masses involved - but you shouldn't be guessing.)

L_{v}=2252kJ/kg
L_{m}=144kJ/kg
C_p = 4.2kJ/kgK (approx 0 - 100C)
for steam (100C+) it can vary a LOT.
http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html