To measure the specific heat capacity of a newly developed alloy, a researcher fits the sample with an electric heater and two thermocouples. The heater is powered by a variable‐output supply. Voltage V across and current I through the heater are recorded every 20 s for a total heating time of 200 s. The data are provided in the table below. The mass of the alloy sample is 0.300 kg; its temperature rises from 22 °C to 58 °C during the heating.
Time (s) | 0 | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200
Voltage (V) | 11.0 | 11.2 | 11.5 | 11.7 | 11.8 | 11.9 | 12.0 | 12.1 | 12.1 | 12.0 | 11.9
Current (A) | 3.20 | 3.18 | 3.15 | 3.14 | 3.12 | 3.10 | 3.08 | 3.07 | 3.05 | 3.03 | 3.02
Assume the only significant energy input to the alloy is the electrical energy delivered by the heater and that energy losses to the environment are negligible.
(a) Using the data, calculate the total electrical energy delivered to the alloy during the 200 s heating period. State any approximations you make.
(b) Determine the specific heat capacity of the alloy.
(c) A materials database lists the accepted value for the alloy’s specific heat capacity as 620 J kg⁻¹ K⁻¹. Calculate the percent error of your experimental value relative to this accepted value.
(d) Discuss one experimental improvement that would most effectively reduce the percent error you found in part (c), and justify how it would do so.