Experiment 7: Temperature Measurement

Temperature and its concept is one of the most intuitive aspects to our lives as human beings. However, much of its behaviour turns out to be not as intuitive as one might think. For one, very few laymen can correctly differentiate temperature from heat, in which temperature is not actually the "hotness" or "coldness" of things, but is in fact an indicator of the direction of heat transfer between two objects. Another non-intuitive aspect of temperature is that it cannot be directly measured. When two objects of differing temperature come into contact, heat will flow from one object to the other. When the exchange of heat no longer occurs, the two objects are in what we call thermal equilibrium. Both objects would be at the same temperature. According the the zeroth law of thermodynmics, if A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then it should follow that A is in thermal equilibrium with C. So when using a thermometer to measure an object's temperature, what is actually being measured is the thermometer's temperature. This does, however, come with consequences. The transfer of heat from the object to the thermometer would mean an decrease in the object's actual temperature. Another would be that getting a reliable temperature measurement is not instantaneous. Depending on the thermometer used, it will take time to make a good measurement since there will be a flow of heat from the object to the device. This may vary from a fraction of a second, to half a minute depending on the nature of the device used. Taking these factors into account, each material has what is called a thermal time constant. This is defined as the time it takes for an object to reach 63.2% of its final temperature. In this experiment, we explored, obtained and analyzed the various time constants of three different types of thermometers. Namely the alcohol thermometer, mercury thermometer, and the thermocouple. The method of choice was pretty simple. For a given thermometer, an initial temperature reading was measured in a glass of ice cold water. Afterwards, a final temperature reading was taken in a pot of boiling water. The desired temperature at the thermometer's yet unknown thermal time constant was solved using the equation



With the desired temperature at hand, the thermometer was brought to its initial temperature then quickly dunked into the pot of boiling water until it reached the temperature solved using the equation. The time it took for that to be achieved was recorded. This recorded time was the thermometer's thermal time constant! Three trials were done for the heating process, while another three trials were done for the reverse - the cooling process. In total, six trials were done for each type of thermometer. All results were tabulated below.

Table 1: Heating of Alcohol Thermometer

Trial	Final temp	Initial temp	T(τ)	τ(s)
1	92	2	58.88	5.38
2	92	2	58.88	5.68
3	92	2	58.88	5.7

Table 2: Cooling of Alchohol Thermometer

Trial	Final Temp	Initial Temp	T(τ)	τ(s)
1	3	92	36.752	10.63
2	4	92	35.384	7.92
3	3	92	35.752	7.05

For the alcohol thermometer, thermal time constant for heating was generally consistent throughout the three trials. A more visible difference, however, was observed in the time measurement of the cooling process. Trial one differed from other two trials by roughly three seconds. Nonetheless, the general trend observed between both processes was that the cooling process took a longer time than the heating process. To account for the error observed, it should be noted that this particular experiment invited a big risk of human error, as the trials generally depended on a lot of error-prone methods of measurement, such as visually observing when the temperatures hit their marks, having to stop the timer once the measurer said so, etc.

Table 3: Heating of Mercury Thermometer

Trial	Final Temp	Initial Temp	T(τ)	τ(s)
1	94	4	60.88	8.87
2	94	1	59.776	10.08
3	94	1	59.776	10.9

Table 4: Cooling of Mercury Thermometer

	Final Temp	Initial temp	T(τ)	τ(s)
1	2	94	35.856	15.86
2	2	94	35.856	22.22
3	2	94	35.856	20.96

The mercury thermometer on the other hand did not display the same precision in results as the alcohol thermometer did; especially in the cooling process, where differences were as high as 6 seconds. However, it was again observed that the cooling process took longer than the heating process. Compared to the alcohol thermometer, the mercury thermometer also had larger thermal time constants. This can be attributed to the mercury thermometer’s bigger dimensions, which indicate more mass.

Table 5: Heating of Thermocouple

Trial	Final Temp	Initial Temp	T (tau)	t (s)
1	99.3	0.6	62.98	0.13
2	98.9	0	62.5	2.3
3	99.3	0.4	62.9	1.35

Table 6: Cooling of Thermocouple

	Final temp	initial Temp	T (tau)	t (s)
1	2	96	36.6	1.48
2	2	96.3	36.7	1.12
3	2	96.3	36.7	3.2

Compared to the last two types of thermometers, the thermocouple’s results varied drastically in duration. All trials for both heating and cooling lasted typically below the count of four seconds. Such results are consistent with existing theory on the transfer of heat. Two main factors can be attributed to such quick thermal time constants. One is the relative size of the sensory nodes of the device. Compared to the sizes of the alcohol and mercury thermometers, the thermocouple’s sensors (two thin copper wires) are only a fraction in overall mass and size. Even intuitively, one can see how it would take much less time to change its temperature. The second factor lies in the fact that the thermocouple is composed of material with particularly high thermal conductivity, which is copper. Copper’s thermal conductivity is set at more than 380 W/mK while the glass used in conventional thermometers is at roughly 1 W/mK. With these two factors at play, it is no doubt that the thermocouple would exchange heat at a faster rate, and thus reach thermal equilibrium faster. With such quick to occur time durations, it should be noted that the precision of the measurements were subjected to more risk of error. This accounts for the relatively greater variation between the results of each trial.

The applications of thermometers and the theory behind how they work can be and is in fact applied throughout our everyday lives. Take for example, the measurement of temperature of someone with a fever. Normally, engineers consider a duration of three thermal time constants to be a reliable time period of measurement. 

Sources:

[1] N.p., n.d. Web. <http://www.chemistryexplained.com/St-Te/Temperature.html>.
[2] "Physics 103.1 Experiment Manuals: Temperature Measurement." National Institute of Physics, n.d. Web.
[3] "Physics 103.1 Experiment Manuals: Heat Conduction." National Institute of Physics, n.d. Web.
[4] "Thermal Conductivity of Materials and Gases." The Engineering Toolbox. N.p., n.d. Web.