Two weeks ago I redid the cooling experiment paying more attention to the precision measurement of the temperature through the use of a thermistor. The experimental setup is shown below with the thermistor inserted in a tall glass of hot tap water.
The thermistor was insulated with heat shrink tubing and held in place by a foam board card. The thermistor resistance was measured with a digital multimeter. The thermistor was obtained from Radio Shack a few years ago and contained calibration data on the back of the card.
A cubic fit of the characteristic curve for the temperature vs the natural log of the relative resistance allowed the resistance measurements collected to be converted to temperatures in °C. The electrical properties of a thermistor can be found in Millman & Halkias, Electronic devices and circuits, 1967, McGraw-Hill, p.132.
The resulting measurements were very consistent.
Using an electrical analogy for the cooling mechanism one can derive a formula involving exponential functions that one can fit to the data. The fit is quite good and also compares well with the rate of internal cooling which is proportional to the negative rate of change in temperature.
The data for the last plot used a numerical formula to estimate the rate of change in temperature.
The results for the experiment were quite good but that doesn't necessarily mean they were accurate since we couldn't check thermistor calibration against a standard gas thermometer or, equivalently, the thermodynamic temperature scale. The ambient temperature of the room remained within a few tenths of 70.1 °F throughout the entire time the data was collected and there may have been a some slight warming towards the end of the data. Although I recorded the data manually the entire experiment could be done with a computer recording the data using a USB port if the appropriate drivers are installed on the computer.
One wonders how accurately the temperatures are measured using weather temperature recording programs?
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