Quantitative Thermal Conductivity

Quantitative Thermal Conductivity 

 Placed 90g of hot water outside the can in cup and 49 g of cold water inside the can then placed the probes as seen above touching the inside of the can wall to measure the heat flow. This experiment will allows us to find the thermal conductivity constant.

The graph on the bottom is showing how temperature changes with respect to time. The linear fit was done by restricting the domain since the data did not appear linear. The slope of the two graphs shows the change in the degrees Celsius per second. The graph on the top is showing the change in Heat per second. In this graph we also restricted the domain to find the slope of the linear part of this graph. The slope of this graph represent dQ/dt, which was used to determine the thermal conductivity (k).

We were able to find the uncertainty of most the variables for the equation dQ/dt=kA(Th-Tc)/L, expect we had trouble determining the uncertainty of Heat (dQ/dt) since it was determined by manipulating the graph in logger pro at the bottom of temp verses time and recalculating to represent heat verses time (graph at top). The picture above shows the equations used for uncertainty of surface area, thickness, temperature, and of the thermal conductivity. But we could not calculate cause we had no way of determining uncertainty of dQ/dt. So we then proceeded to use the values without the uncertainty to get a rough estimate of what the thermal conductivity would be. As you can see above we found k=0.02 W/m*C. The true value of k for aluminum is k=205 W/m*K. The large error in our result may be due to the fact that we did not as a group understand how to accurately find the uncertainty in the equipment.