Thermal Model: Mug Project

Math Models:

As I begin to create a math model I look to the key concepts of the subject that I am trying to derive equations for, starting with the knowledge that I already know as a point to expand from.  For example with this thermal mug project our equations will be derived from the fundamental laws of thermodynamics.  I know from my chemistry class that our enthalpy equilibrium equations are applicable in this scenario.  As ice and water are placed into the same system we see an averaging of the kinetic energy in the molecules of the solid and the liquid.

I identify all of my known and unknown variables.  Once I know how many variables that I have to solve for, I know how many equations that I need to find in order to come to my final solution.  I try to identify everything affecting the system I am working in and combine my equations to find my final solution/solutions.

>> temp
Jenny Madsen
Temperature equilibrium equation
What is initial temperature of the liquid?85
What is initial temperature of the ice?-13
How much does the ice weigh?.102
How much does the water weigh?.228
   83.9634


ans =

   83.9634

function [Tfin]=temp(TinW,TinI,Mi,Ci,Mw,Cw,Hsf)
disp('Jenny Madsen')
disp('Temperature equilibrium equation')

TinW=input('What is initial temperature of the liquid?');
TinI=input('What is initial temperature of the ice?');
Mi=input('How much does the ice weigh?');
Mw=input('How much does the water weigh?');

Cw=4.186; %Kjoules/Kg*degrees C
Ci=2.09; %Kjoules/Kg*degrees C
Hsf=334; %Kjoules/Kg*degrees C

Tfin=(-TinI*Mi*Ci-TinW*Mw*Cw+Mi*Hsf)/(Cw*(Mi-Mw));

disp(Tfin)

Conclusion:
This value is not the value that I expect my equation to reflect.  I have done some modification that seems to be helping but the equation needs to be adjust somehow.  It might be for using kelvin or I may have a sign or division error somewhere.  It shouldn't take much improvement to reflect my expected values for use in testing and analysis though.