In the Classroom
The Thermometer as a Simple Instrument George F. Atkinson* Department of Chemistry, University of Waterloo, Waterloo, ON N2L 3G1, Canada
How do you introduce students to the basic ideas of instrumental measurement and to the idea of a measurement instrument? One approach I have found successful is to begin with the familiar liquid-in-glass thermometer. The ideas here are straightforward and do not depend on prior knowledge of electricity, optics, or electronics. The purpose of this short paper is to show some of the ideas that can be drawn from a careful investigation of the thermometer. Instrumental measurements usually depend on finding some practically measurable physical phenomenon that is related in a known and reproducible way to the quantity, property, or other characteristic we wish to know about. In this case, the expansion of a liquid when heated is used to give information about the temperature of the sample material. Therefore, we need to know the coefficient of volume expansion of the thermometric liquid, usually mercury or alcohol and occasionally pentane, and whether this coefficient is itself variable with temperature. In this paper, we will assume mercury has been chosen. If numbers are to be reported, we must establish a scale for measurement. This requires at least two agreed quantities: a scale unit and a reference point. In this case, the customary scale unit is the Celsius degree. The common reference points are the two readily available ones related to our most common liquid: the triple point of pure water and the boiling point of water at one atmosphere pressure. If the thermometer is to be used in other ranges, other suitable points of the International Temperature Scale (ITS-90) may be selected. The scale is described in the CRC Handbook of Physics and Chemistry 76th edition 1995–96, pp I-16–I-17. Some principal points of this scale are, in °C: Oxygen point (boiling point of liquid oxygen) ᎑182.97 Triple point (ice, water, and water vapor) 0.01 Gallium point (melting point) 29.7646 Steam point (at 1 atm pressure) 100 Indium point (melting point) 156.5985 Tin point (melting point) 231.928 Zinc point (melting point) 419.527 Antimony point (melting point) 630.5 Silver point (melting point) 960.8 Gold point (melting point) 1063.0
Once we know the desired range of readings and the desired smallest readable scale unit, we can calculate the necessary scale length along the thermometer stem, the necessary volume of mercury for a given diameter of mercury column, and the necessary volume of the thermometer bulb below the scale, which must contain the rest of the required mercury. To devise an optimum physical design of the device, we also need to know the best shape for the bulb. Should it be spherical for maximum strength, or a long narrow cylinder to maximize the proportion of the mercury close to the wall separating it from the sample, which will speed the attainment *Deceased.
of a final reading? Two more factors are thus introduced that apply generally to measurement instruments: conditions of use (sometimes better thought of as ability to withstand abuse) and response time. At this point, we might turn our attention further to the enclosing material: glass. Close observation of the mercury level when a thermometer is first put in contact with a warmer sample, say of water, shows that the mercury first goes down slightly, and then starts to go up. Why? What is the first thing warmed by the water? Obviously, the glass. What does it do? It expands—the bulb becomes larger and some mercury from the stem (where the scale is) recedes into the bulb before the mercury itself begins to be warmed and thus to expand. Obviously this must be allowed for in establishing the scale on the stem. So must the fact that as the sample warms the stem of the thermometer, the stem becomes longer by thermal expansion. Clearly, the scale of an accurate thermometer will need to be calibrated at a series of accurately known temperatures and provided with a table of corrections. Now what about emerging-stem correction? The portion of the thermometer being read is usually not immersed in the sample. Some thermometers bear an inscribed label “76 mm immersion” and an engraved line 76 mm above the bottom of the bulb. These have been calibrated with the sample bath at that line. Other thermometers usually assume total immersion in the sample, and when not so used, may require an emerging-stem correction. Details that will be found in older physics texts or books on thermometry usually begin with an auxiliary temperature reading taken midway along the stem between the immersion level and the reading level. Now let’s consider heat transfer and heat capacity. Students will know heat transfer in glass is poor. A glassworker can comfortably hold his work a few inches from the point where it is red hot or even white hot. This also plays a role in emerging-stem correction, just discussed. It therefore seems wise to make thermometer bulbs as thin as possible. The heat transfer in mercury, as in most solid metals, is much better. However, its heat capacity is large. A large volume of mercury, capable of giving a sensitive temperature reading (say in a Beckman differential thermometer), is also capable of withdrawing significant heat from a small sample, thus providing inaccurately low temperature readings. Think of a fly landing on the bulb of a Beckmann thermometer. We will not read the fly’s temperature—the fly will simply get cold feet! This suggests that the volume of mercury should be kept as small as possible. The point that every instrument is likely to perturb the measurable property of the sample is thus introduced. What about artifacts? Take the bulb of the thermometer gently between your thumb and finger and squeeze it several times. The mercury will rise and fall in response to pressure on that desirably thin glass wall. The reason for installing thermometer wells in apparatus to isolate thermometers from even rather modest internal pressures is thus shown. Stability of the instrument? On this point, students are told of the descriptions in manufacturers’ catalogs of how glass thermometers are stress-relieved by annealing after being
JChemEd.chem.wisc.edu • Vol. 75 No. 7 July 1998 • Journal of Chemical Education
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In the Classroom
blown and then “seasoned” through temperature cycles before being calibrated. The availability of National Institute of Standards and Technology (NIST) and NIST-traceable certification and the procedures used in certifiable calibration are also discussed. I have used this discussion of the liquid-in-glass thermometer in two courses that I have taught. In one course, this discussion has been used as a lead-in to dealing with electrical
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methods of temperature measurement using resistance thermometers, thermistors, and thermocouples. Both the analogous problems and the new problems introduced by the electrical system are discussed. In another course, this material is used immediately after a general description of the nature of an instrumental measurement. In both cases, the students respond well and are appreciative of the discussion of this (notso) simple case before tackling more complicated ones.
Journal of Chemical Education • Vol. 75 No. 7 July 1998 • JChemEd.chem.wisc.edu
