Last month I described how to build a triple-point cell, a device that reproduces the unique temperature, defined to be exactly 0.01 degree Celsius, at which water can exist with its solid, liquid and vapor phases all in equilibrium. The cell can be used for calibrating state-of-the-art thermometers, but few amateur scientists can afford such expensive instruments, which cost thousands of dollars.

Fortunately, George Schmermund, the creative genius from Vista, Calif., who developed our triple-point cell, has also designed a thermometer capable of measuring temperature to within a few thousandths of a degree C. What is more, you can build this remarkable instrument for less than $100.

Schmermund's thermometer uses something called a resistance temperature detector (RTD), which relies on the fact that the resistance of platinum changes with temperature in a precisely known way. For each degree C of temperature change, these sensors typically change their resistance by 0.00385 ohm per ohm of resistance. For example, if your RTD has a resistance of 100 ohms, each degree C change in temperature will alter the resistance by 0.385 ohm. So if you know the probe's resistance at a particular temperature, such as the triple point of water, you can then convert any measured resistance into a corresponding temperature.

Image: DANIELS & DANIELS EXACT TEMPERATURE MEASUREMENTS to within millidegrees can be made with a thermometer that relies on a resistance temperature detector (RTD)--a sensor that exploits how the electrical resistance of platinum changes as the material becomes hotter or colder. The relation is linear and is given by the equation shown (above), where a (Alpha) is typically 0.00385 and RTP is the resistance of the sensor at 0.01 degree Celsius: the triple-point temperature of water. A digital multimeter measures the RTD's resistance.

In the past, RTDs were always made of wire. Because the wire had to be thick enough to withstand the manufacturing processes and because a larger-diameter wire has less resistance than a smaller one made of the same material, the operating resistance was limited to about 100 ohms. Recently, though, a new breed of RTDs has been constructed by laying an ultrathin platinum coating on a ceramic substrate. The resistance of some of these devices tops 2,000 ohms. You'll find a smorgasbord of these marvels in the catalogue of Omega Engineering in Stamford, Conn. (www.omega.com; 800-826-6342). For this project you'll need a model like the F3141, a small, unencapsulated 1,000-ohm unit that sells for $19.

These new RTDs can bring exquisite sensitivity into the home-based laboratory. Using a high-quality handheld digital multimeter that can measure 1,000 ohms of resistance to within 0.02 ohm, amateurs can now resolve temperatures to within 0.005 degree C, or 0.009 degree Fahrenheit. That performance bests liquid-filled thermometers by 20 times and trumps any thermocouple by a factor of 10.

And you can do much better. In practice, the sensitivity of an RTD-based thermometer is limited by how accurately you can determine its resistance, which is measured by observing the voltage drop associated with a known current. With a typical digital multimeter, the lead wires are part of the circuit, and so their resistance affects the results. This error can be eliminated by measuring the voltage drop directly across the resistor with an independent set of wires. Such instruments, called four-wire ohm meters, have separate inputs for a current source and a volt meter

Image: DANIELS & DANIELS RTD SENSOR ASSEMBLY comprises an RTD sensor connected to two bent nickel wires that are threaded through four capillary tubes.

Hewlett-Packard's snazzy HP 34401A multimeter (priced at $995) uses the four-wire technique to measure 1,000 ohms to within 0.001 ohm. And top- of-the-line instruments costing $30,000 apiece enable professionals to resolve temperature differences as slight as 10 millionths of a degree C. In such a four-wire configuration, an RTD-based thermometer is called a standard platinum resistance thermometer (SPRT).

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