| 12 | Copper cylinder in hot water |
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| Main | A cold copper cylinder is submersed in hot water. The water is inside a glass container inside a heavily insulated cylindrical container. A magnetic stirrer is used to make sure the water is always well mixed. The temperatures of the water and of the inside of the copper cylinder are recorded as functions of time. More…
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| Description | DESCRIPTION OF EXPERIMENT |
| Experiment | A cold copper cylinder is submersed in hot water. The water is inside a glass container inside a heavily insulated cylindrical container. A magnetic stirrer is used to make sure the water is always well mixed. The temperatures of the water and of the inside of the copper cylinder are recorded as functions of time. The thermometer for the copper is inserted in a hole near the center of the cylinder.
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| Dimensions | Water: Mass: 796 g Copper cylinder: Mass: 2760 g; Radius: 30 mm; Height: 110 mm Thermocouple in cylinder: Depth: 50 mm; Distance from center: 10 mm Glass container: Mass: 193 g; Inside diamter: 9.00 cm; Thickness: 1.5 mm Glass container: Height: 15 cm Insulation (cotton): 23 mm Aluminum (outside): Inside diameter: 14.0 cm; Thickness: 1.0 mm Bottom and lid (styrophoam): 20 mm |
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| Assignment | A POSSIBLE PATH THROUGH THE INVESTIGATION… |
| Basics | Investigate the experiment, make sure you understand the setup of the system and the initial conditions. Plot the data to get a feeling for the dynamical process. Estimate time constants of the processes. Create a word model for the system and its processes. Create a formal dynamical model. Import data, simulate the model and determine the parameters of the model by comparing simulation and experimental data.
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Particulars | Compare model and virtual and/or experimental data to determine the entropy capacitance (and the specific heat) and the conductivity of copper. The temperature of the copper cylinder was measured close to its central axis. How good is a model representing the cylinder as a single uniform body for predicting the temperature a its center? Propose changes in the model if you are not satisfied with the agreement between model and data. |
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| Model | MODEL EQUATIONS AND MORE… |
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| Questions | SOME SIMPLE QUESTIONS… |
| 1 | Assume that the experiment was performed with a copper cylinder of twice its mass. How would the process of temperature equilibration differ from the one observed? |
2 | Which quantities of the systems are relevant for the final equilibrium temperature? |
3 | Which quantities of the systems determine how fast the equilibrium temperature is attained? |
4 | Consider the equilibration of temperatures of water and copper (no other bodies involved). Basically, we produce RC-models to understand the phenomenon. In simple RC-models, we can only determine the product of R and C, not R and C separately. Does this mean that we cannot determine the conductivity and the specific entropy capacitance of copper separately in an experiment such as this one? Assume the specific entropy capacitance of water to be known. |
5 | Copper is a very good thermal conductor. Still, the temperature of the copper cylinder could not be the same at every point inside during the experiment. How could you model the process of temperature equilibration between water and copper taking account of the fact that the copper cylinder is inhomogeneous during the heating? |
6 | Consider the copper cylinder immersed in water to have the same temperature as the water. We know that it would be impossible for the water to become hotter and the copper cylinder to get colder spontaneously. What is the reason for this? Is it because there is no energy that can be released to drive the process, or is it because in the reverse process entropy would have to be destroyed? |
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