The first thing I do when making math models
is outline the situation and goal of the model. Secondly, I brainstorm the physics
involved in the situation and then I relate those to equations all mentally and
verbally. Then I organize my thoughts by writing down the equations and
defining the variables. Then I start algebraically manipulating the equations
until I have isolated the desired variable. Lastly, I put my equation into a
calculator or computer program with some example values of which are easily
testable or relevant to life. I then compare my values to experimental values
to check the accuracy of the model. In this case I created a function for my
model in Matlab. As I am a college student I actually don’t really have the
resources of testing the situation in a common application easily, and I was
unable of finding someone else’s results of a similar experiment, so I was
unable to test my model in a timely manner
Math
Model in Matlab:
For this example, the container
is a large glass beer mugs, of which tend to weigh around 2 lbs (about 900g), the
mug was in a common household freezer and 250 ml/g of water (about 8 ounces) at
room temperature is poured into the mug.
Matlab
Script:
function T=
thermal(Mw,Mc,Cc,Toc,Tow)
Mw=.001*input('amount of
water [g]');
%requests for the mass of
water and converts from g to kg
Mc=.001*input('mass of
container [g]');
%requests for the mass of
container and converts from g to kg
Tow=input('initial
temperature of the water [C]');
%requests the initial
temperature of the water
Toc=-20.5; %common
temperature of household freezers [C] (exemplary value)
Cc=.84; %specific
heat of glass (exemplary container material [kJ/kg*C)
T=(4.18*Mw*Tow+Mc*Cc*Toc)/(4.18*Mw+Mc*Cc)
%the final temperature of
the glass and water
Command
of Model:
>> thermal;
amount of water [g]250
mass of container [g]900
initial temperature of the water [C]23
T =
3.9006
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