Monday, November 5, 2012

My Thermal Mug Math Model

 I constructed a math model for the following situation: "Warm water (an idealization of beer or soda) is poured into a container (an idealization of a chilled mug) that has been placed in the freezer. The system (i.e. mug plus water) is allowed to reach thermal equilibrium."
             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

 The situation is from Dr. Don Elger's website learning4doing.com

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