Vensim Modeling: Build a VenSim model for Newton’s Law of Cooling, which says that the change in temperature is proportional to the difference between the object’s temperature and the temperature of the environment surrounding it. Furthermore, this change in temperature of the object is proportional to a constant specific to the material, called the thermal conductivity. dT/dt = -k(T-T room) T(0)=T0 if T(0) = 200 C, room temperature is 20 C, and k = 0.25, how long does it take for the temperature to reach 110 C (midway between T(0) and room temperature)? If T(0) = 100, room temperature is 20 C, k = 25, how long does it take for the temperature to reach 60 C (midway between T(0) and room temperature)? Answer the above questions for a different material, one which has k = 0.025. Show the VenSim diagram and only one of the plots of T vs t. Make sure your plots are properly labeled (titles, plot labels) Briefly comment on the model (for example, how realistic is this model – under what assumptions is it good? Describe how the model works if you’re describing a frozen steak removed from the freezer. What do your answers to (a) and (b) tell you about this physical system? Can you give an analytic solution to this system – that is, can you write down a function which satisfies this problem?)

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Vensim Modeling: Build a VenSim model for Newton’s Law of Cooling, which says that the change in temperature is proportional to the difference between the object’s temperature and the temperature of the environment surrounding it. Furthermore, this change in temperature of the object is proportional to a constant specific to the material, called the thermal conductivity.

dT/dt = -k(T-T room)

T(0)=T0

if T(0) = 200 C, room temperature is 20 C, and k = 0.25, how long does it take for the temperature to reach 110 C (midway between T(0) and room temperature)?
If T(0) = 100, room temperature is 20 C, k = 25, how long does it take for the temperature to reach 60 C (midway between T(0) and room temperature)?
Answer the above questions for a different material, one which has k = 0.025.
Show the VenSim diagram and only one of the plots of T vs t. Make sure your plots are properly labeled (titles, plot labels)

Briefly comment on the model (for example, how realistic is this model – under what assumptions is it good? Describe how the model works if you’re describing a frozen steak removed from the freezer. What do your answers to (a) and (b) tell you about this physical system? Can you give an analytic solution to this system – that is, can you write down a function which satisfies this problem?)

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