University of the West of England
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Propagation of Uncertainty (Calculation of thermal capacity)

In an experiment to measure the specific heat capacity, c (J kg-1 oC -1), of a material, a body of mass m (kg) is heated electrically using a voltage, V (volts), and current, I (amps), for a time, t (s). The temperature of  the body rises from T1 to T2 (oC).

The specific heat capacity of the body is given by the equation:

 i) Develop a spreadsheet model that will enable you to calculate the following set of results: value, standard deviation uncertainty (SD), relative uncertainty (CV%), and 95% confidence interval of the specific heat capacity, c. Within your model, you should calculate explicitly the uncertainty in the value of (T2-T1). The layout and structure of your spreadsheet should be such that the procedures for calculation are quite explicit and can be easily understood by someone else who wants to follow your calculations. ii) Record the above results for the following input values (including standard deviation uncertainties): I  =   10.60 ± 0.02 amps V  =  12.0 ± 0.1 volts t  =   120 ± 1 s m  =  0.68 ± 0.01 kg T1 =  45.6 ± 0.1 oC T2 =  40.4 ± 0.1 oC iii) Decide, with explanations, which of the following experimental improvements would be the most effective in improving the accuracy of the overall measurement: a)         Improve the accuracy of the measurement of mass to ± 0.001 kg OR b)         Improve the accuracy of the current measurement to ± 0.002 amps OR c)         Improve the accuracy of both temperature measurements to ± 0.05 oC