Physics lab: how do i find the uncertanity of c (specific heat of water)

Question

Physics lab: how do i find the uncertanity of c (specific heat of water) , when this is the data i have: I have the mass of water= 0.2304 kg, I have the temp for every 15 second time interval, i have the Q (heat energy) for for every 15 second time interval, I ploted a regression line Q vs Delta TEmperture data and got a slope and with the slope i solved for c (specific heat of water) and got 4438 J/(kg* degrees C), The accepted value for c is 4180 J/kg oC. how do i calculate the uncertanity of specific heat?

Answer 1

Hi Lilly B.,

"Uncertainty" is a vague term here. There's indeterminate error in measurements, and determinate error in other things (probably the larger source of misagreement between your data and the accepted value). Let's look at some (not having viewed your apparatus, I won't catch them all!) of the potential sources of error. Temperature: uncertainty in actually reading/transcribing the output value: if you have an analog thermometer, this is the precision +/- one half a precision unit (so, if ruled each 0.1C, then +/- 0.05C). These errors balance out over many multiple data, but still leave some indeterminate line-fit slop. But you may have determinate error also, if you didn't sight your thermometer level. If you had a constant mis-sighting angle on your thermometer, that won't affect your regressed line slope, though. Potential error in linearity of thermometer: probably beyond your ability to assess; you would have to calibrate across at least your usage range using an accurate reference thermometer, such as a platinum resistance probe. But this is probably a minor contribution. Next: error in distributing the heat input properly throughout the calorimeter. This is potentially large; a substantial stirring rate is needed. Flow patterns may not be apparent, and so on. Impossible to estimate without some experimentation. Next: Error from the set of regressed points used, due to non-steady-state rate of change being achieved. If you just turned your heater on at time 0, and took a data point there, you certainly won't be able to use that point. You might be able to examine your data and select a set which will give a very-close-fitting regression line, making sure to discard early points which lie consistently on one side of that line. Last: You know your mass of water, BUT what about the heat capacity of the rest of your heated calorimeter components -- container, stirrer, thermometer, etc.? That's probably what's killing your agreement to the accepted value. How could you test? You could, using different water fill amounts -- the heat capacity of the other stuff will remain constant, but the heat capacity of the water will scale with the mass of water, obviously.

So -- to summarize -- when you discuss, and note the uncertainty contributed by all the minor things like data point scatter, indicate that those are indeterminate error. If you find a curvature on your plotted/regressed data points, that's a determinate error ( an "oops!"). And the big one, the heat capacity contribution by the rest of the equipment, that's determinate error also (really an "oops" on the part of the experimental design, but a learning opportunity!) -- Mr. d.