Temperature Measurement

Expansion-Contraction Thermometers

Galileo is credited with inventing the first density-based thermometer, the thermoscope. In an open container of alcohol, he placed a long glass tube with a sphere at the upper end into this liquid after warming the sphere with his hands. The air in the sphere would then cool and contract, drawing alcohol into the tube. Then as the air temperature changed, the air in the sphere would expand or contract causing the colored alcohol to move up or down in the tube. Modern day Galileo thermometers use sealed vials of various densities in a liquid. As the temperature rises and the density of the liquid decreases, more of the vials sink to the bottom. The temperature can be read by marking each of the vials in turn.

Following the thermoscope, water-based, open-ended thermometers were used. These were superceded by closed-glass liquid thermometers much like those we use today. Mercury was chosen for precision thermometery due to its uniform expansion.

In the mid 1700's, John Harrison invented the bi-metallic strip for temperature compensation in clocks. Two metals with different coefficients of expansion are bonded together. Heating them equally will cause the strip to bend in one direction, cooling will cause them to bend in the other direction. The deflection can be used to indicate temperature. This device is widely used in thermostats and breaker switches. Helical bi-metallic springs are used in dial thermometers.

Resistance Thermometers

The electrical resistance of metals is strongly temperature dependent (the resistance increases with increasing temperature). The most accurate thermometers use the resistance of platinum as the measured indicator. The laboratory standard is known as the "bird-cage" element. A helical platinum coil is suspended in a cage-like configuration to minimize strain-induced resistance changes. A more robust construction uses a film of platinum deposited on a ceramic substrate.

The resistance of a platinum thermometer is low (10-100 ohms) and the temperature coefficient is also low (0.385 ohms/C at 0C) so the resistance measuring equipment must be sensitive and accurate. The resistance of the connecting wire must be minimized since it can have a dramatic effect on the measurment. The usual method for measuring resistance with with a Wheatstone Bridge where the platinum resistor forms one arm of the bridge. A three wire bridge is used to control for any temperature effects on the leads going to the thermometer.
Fig. 14.2.1 Three Wire Bridge

Resistance is converted to temperature using the following formula:

where RT is the resistance at T, R0 is the resistance at 0C, alpha is the temperature coefficient at 0C (typically 0.00392 ohm/ohm/C), delta is 1.49 (typically), and beta is 0 for positive T and 0.11 for negative T.

The problems encountered with resistance thermometers include self- heating (must be subtracted from the measurement), thermal shunting (heat is conducted away from the system), and slow response time.


Thermocouples depend on the Seebeck effect in which the heating of a junction of dissimilar metals produces a potential difference between the two metals. The difficulty encountered when trying to measure this voltage is that new thermoelectric junctions are created when the measuring apparatus is connected to the circuit. To get around this, two junctions are used, so that the metal that attaches to the voltmeter is the same in both cases (copper is usually used). One of the junctions is held at a constant reference temperature so that the voltage produced by the other junction will be independently measurable.

Fig. 14.2.2 Thermocouple with an External Reference Junction

Since the Seebeck voltage is approximately linearly proportional to temperature, the resulting voltage will be proportional to the temperature difference between J1 and J2. The external reference temperature is usually an ice-water bath, since it gives a precise reference temperature of 0C.

Practical thermometers usually do away with the ice-water bath reference by introducing a room-temperature reference junction with a thermistor. Although a thermistor is not useful over as wide a range as a thermocouple, it is perfectly adequate for the limited temperature range encountered in a modern laboratory. A constant voltage source (from a battery) is fed through the thermistor to provide an output that is identical to that produced by an ice-water reference junction.

Fig. 14.2.3 Thermocouple with an Artificial Ice-Point Reference Junction

Over a wide range of temperatures, thermocouple voltage can be highly non-linear. Temperature interpolation is usually derived from polynomial fits of around 7th order.

Small diameter thermocouples can have a very fast response time; the devices are rugged, inexpensive, and cover a wide range of temperatures. Problems with thermocouples include thermal shunting and galvanic action (dyes from thermocouple insulation can form an electrolyte in water, causing a galvanic voltage that overwhelms the Seebeck voltage).


Thermistors are semi-conductors with a negative temperature coefficient (resistance decreases with increasing temperature). They are highly sensitive to changes in temperature, but their range is more limited than thermocouples or resistance thermometers. The response of thermistors is highly non-linear and is thus more easily incorporated into computer-driven thermometry. An individual thermistor curve is usually approximated by the Steinhart-Hart equation:

Where T is the absolute temperature, R is the resistance, and A,B,& C are fitted parameters.

For speed of computation, this is often simplified to:

A, B, & C are found by selecting three data points on the published data curve and solving the three simultaneous equations. With a 100C range, the Steinhart-Hart equation will approach an accuracy of +/- 0.02C; the simpler equation requires a smaller range if the same accuracy is desired.

Semi-Conductor Thermometers

Integrated circuit temperature sensors have recently become popular due to the ability to incorporate them into standard chips. They make use of temperature dependent oscillators, so a simple count is all that is required for temperature measurement. Since the sensor is part of an integrated circuit, it is simple to put electronics for signal conditioning, including a processing unit with microcode, on the same chip. They are now cheap and readily available. The Dallas Semiconductor DS1820 is an example of just how useful these devices are.

Infrared Temperature Measurement

All objects emit black-body radiation as a function of their temperature. For objects that are not incandescent, this radiation is in the infra-red range. Optical sensors are now available to measure IR radiation and optical lenses are available to focus it. The result is a remote temperature measurement device with a fast response time (100 msec). They can be used for any object with an emmissivity greater than 0.1 (polished metals or mirrors will give inexact readings).

Comparison of Methods of Thermometry

ThermocoupleResistance Thermometer ThermistorIC Sensor
Advantages Self-powered
Wide variety
Wide temperature range
Most stable
Most accurate
Fairly linear
High output
Simple measurement
Most linear
Highest output
Disadvantages Non-linear
Low voltage
Reference required
Least stable
Least sensitive
Current source required
Small change in resistance
Low absolute resistance
Self heating
Limited range
Current source required
Self heating
T < 200C
Power supply required
Self heating

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Document last updated Mar. 23, 1999.
Copyright © 1999, Ken Muldrew.