Exercises with the Model of Water Temperature

1. Verification:

Build the heat flow model and verify the results shown in Figure 5.

2. Longer Term Expectations:

What do you expect will happen if we allow the simulation to continue for another hour or two? Will the water temperature eventually reach 20 degrees? Run the model for two hours to see if the simulation results match your expectations.

3. Equlibrium Diagram

If the water temperature reaches equilibrium, draw an equilibrium diagram to confirm that the HeatFlowIn is countered exactly by the HeatLoss.

4. Thinner Glass:

The 0.5 cm thickness is much thicker than typical glass containers, so run the model with the thickness set at 0.25 cm. Before performing the new simulation, pencil in the likely results on a time graph from the 1st exercise. Then run the model with the new value of the thickness. Do the simulation results match your expectations?

5. Derive the Long Term Temperature Difference:

Write an algebraic expression that will permit you to derive the 0.08 degrees as a combination of the physical parameters (such as the glass thickness and conductivity). Check the algebraic expression to see if it gives the same results as in exercises #2 and #4.

6. Experimental Verification with a Standard Thermometer:

A simple glass thermometer might reveal a temperature difference of 0.2 degrees. Suppose you wish to design an experiment where the expected temperature difference is at least 0.2 degrees, and you have glasses of many different thicknesses in your laboratory. How thick must the glass be to yield a measurable temperature gap?