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### Simple Devices for Measuring Temperature

One goal of thermodynamics is to minimize the amount of experiment that must be done, though measurements cannot be eliminated completely. Experiments necessarily reveal and quantify the rich behavior of materials. Moreover, experiment both motivates and guides theoretical efforts aimed at interpreting and correlating phenomena. Even when theoretical models are reliable, experimental data are needed to provide values for parameters in the models. Thus, thermodynamics is intimately and irrevocably tied to experiment.

This article provides a superficial introduction to common devices for measuring temperature. We do not delve into experimental protocols; for a more thorough introduction to temperature measuring devices, see Benedict [1].

Absolute temperature is defined to be the average kinetic energy of the molecules making up a system. For example, for a sample of argon gas containing N molecules, the absolute temperature T is defined by

(1)

Here m is the mass of one molecule and vi is the velocity of molecule i. Thus, the rhs is the average kinetic energy of the molecules. The quantity k is Boltzmann's constant, k = R/NA, where R is the gas constant and NA is Avogadro's number.

There is no way to directly measure molecular kinetic energies, and so we always measure temperatures indirectly by measuring some macroscopic consequence of a temperature change: an expansion or contraction of a liquid, a change in pressure, or a change in some electrical property. In fact, any property that changes with temperature may, in principle, serve as the basis for a thermometer. Yet, in spite of the many possibilities, thermodynamics assures us that there is an absolute temperature scale independent of the particular quantity actually measured [2]. Here we briefly discuss three devices: gas thermometers, resistance thermometers, and liquid-in-glass thermometers.

##### 1. Gas Thermometers

These devices use a gas as the thermometric fluid and operation is based on the ideal-gas law, PV = NRT. Thus if either the pressure or the volume is held constant, then measuring the other allows us to determine the temperature. Here we describe the constant-volume apparatus.

The constant-volume gas thermometer consists of a rigid vessel connected by capillary tubing to a pressure measuring instrument, as in Figure 1. The vessel is loaded with an amount of gas, typically hydrogen, nitrogen, or argon. If very low temperatures are to be determined, helium may be used. In principle, neither the amount of gas loaded nor the volume of the vessel need to be known.

Figure 1. Simple schematic of the constant-volume gas thermometer.

First, the vessel and gas are brought to a reference temperature To and the gas pressure Po is measured. This reference condition is often some easily reproduced physical situation whose temperature is known independently of any measuring device. The triple point of water is usually used because the triple point is fixed at 273.16 K on the absolute Kelvin scale.

After Po has been measured, the vessel and gas are brought to the neighborhood of the desired temperature T and the corresponding pressure P is measured. Now, if the gas is ideal and if neither the amount of gas nor the volume of the system (vessel plus tubing) have changed between the two pressure measurements, then the ideal-gas law requires

(2)

and the unknown temperature can be found by

(3)

Thus the principles of constant-volume gas thermometry are straightforward. However, in practice the above three premises are not valid and corrections must be made to achieve accurate results. The corrections include the following:

• The gas will not be exactly ideal, and the degree of nonideality must be taken into account (often by using the virial equation of state).
• Corrections must be made for thermal expansion or contraction of the vessel when the temperature is changed from To to T.
• The amount of gas in the system can change because some gas may absorb onto the walls of the vessel. It is difficult to accurately account for absorption effects and these probably cause the largest uncertainty.

Nevertheless, gas thermometry is a highly accurate means for measuring temperatures: with care, uncertainties can be reduced to ±0.002 K at 300 K. Their useful range is from about 10 K to about 1200 K. However, gas thermometry is tedious and is used mainly as a primary standard: other thermometers are often calibrated relative to gas thermometers.

##### 2. Resistance Thermometers

These devices exploit the fact that the electrical resistances of metals change, in reproducible ways, with temperature. The metal of choice is platinum because it can be made very pure, it is stable and does not oxidize easily, and its resistance varies smoothly over a wide range of temperatures. Consequently, after calibration, the platinum resistance thermometer can achieve highly reproducible readings.

The sensor is formed from fine platinum wire, typically about 0.1 mm diameter and 2 m long. This yields a resistance of about 25 ohms at 0°C. The wire is wound into a helical coil and the coil is wrapped onto a mica support that is about 4 mm (0.2 in) diameter and about 25 mm (1 in) long. The sensor is housed in a glass or quartz tube. Resistance is measured by passing an approximately 1 milliamp current through the wire.

This design can be used from about 100 K to about 1000 K, with accuracies of ±0.001 K, but the instrument is fragile. Suitable modifications can extend the range to either lower or higher temperatures, but those more rugged instruments typically achieve less accurate measurements.

##### 3. Liquid-in-Glass Thermometers

These devices use the thermal expansion and contraction of a liquid to indicate temperature. The liquid most often used is mercury, but colored organics are often used to measure low temperatures. The capillary space above the liquid is filled with nitrogen to prevent the liquid column from separating during temperature fluctuations and in high temperature situations.

The expansion of the liquid is primarily caused by the temperature of the bulb, but it is also influenced by the temperature of the stem. Thus, the scale reading changes when the thermometer's depth of immersion is changed. Liquid-in-glass thermometers are typically designed to be used at one of three immersions:

• partial immersion, in which the device is immersed exactly to a line scribed on the glass,
• total immersion, in which the device is immersed to the top of the liquid column, and
• complete immersion, in which the entire device is immersed.

If a particular device is used incorrectly, for example if a complete-immersion thermometer is only partially immersed, then stem corrections must be applied to correct the scale reading.

The range of a mercury-in-glass thermometer is limited at the low end by the freezing point of mercury (−39°C) and at the high end by the softening point of the glass stem. The best mercury-in-glass instruments can achieve accuracies of about ±0.01 K at 300 K, but this falls to about ±0.2 K at 700 K.

Other common devices for measuring temperature include the thermocouple, which detects changes in electrical potential developed by two metals, and the crystal thermometer, which detects changes in the resonant frequency of a piece of vibrating quartz. These devices must also be calibrated.

Finally, we emphasize the important distinction between measurement and control. Typically the temperature of a system is controlled by immersion in a stirred-fluid bath; the fluid may be gas or liquid. In such devices it is not unusual to be able to control the temperature to within ±0.002 K, as measured by a resistance thermometer. However, accurate measurement of temperatures to less than ±0.01 K requires unusual care.

By the way, the claim for the world's tallest thermometer (135 feet) stands at Baker, CA, on I-15 between Barstow and Las Vegas. It was built in 1991 by the Young Electric Company. Here's a link to a photo: Tall Thermometer

##### Literature Cited

[1] R. P. Benedict, Fundamentals of Temperature, Pressure, and Flow Measurements, 3rd ed., Wiley, New York, 1984.

[2] J. Kestin, A Course in Thermodynamics, vol. 1, Hemisphere Pub. Co., New York, revised printing, 1979, Ch. 2.