Temperature and Thermometers: Scales, Calibration and Types

Measuring How Hot Something Is

A nurse checks a patient for fever, a baker sets an oven, an engineer monitors a furnace at 1200 °C, and a scientist records the temperature of liquid nitrogen. Each needs a different instrument, but all of them work on the same principle: some property of a material changes in a regular way with temperature, and that change can be measured. This tutorial covers temperature and thermometers as tested in WAEC, NECO and JAMB physics: temperature and heat, thermometric properties, fixed points and calibration, the Celsius, Fahrenheit and Kelvin scales, liquid-in-glass thermometers (mercury and alcohol), the clinical thermometer, Six's maximum and minimum thermometer, thermocouples, resistance thermometers, the constant-volume gas thermometer and pyrometers, with worked calculations.

Temperature and Heat

Temperature is a measure of how hot or cold a body is. At the particle level, it measures the average kinetic energy of the particles. It decides the direction in which heat flows: always from a higher temperature to a lower one.
Heat is energy transferred because of a temperature difference. It is measured in joules.

A bucket of warm water holds more heat energy than a cup of boiling water, but the cup has the higher temperature. Two bodies in contact reach thermal equilibrium when they are at the same temperature, and no more heat flows between them. A thermometer works because it reaches the same temperature as whatever it touches.

Thermometric Properties

A thermometric property is a physical property that changes continuously and measurably with temperature. Each type of thermometer uses one:

The length (volume) of a liquid column: liquid-in-glass thermometers.
The electrical resistance of a metal wire: resistance thermometers.
The e.m.f. produced at a junction of two different metals: thermocouples.
The pressure of a gas at constant volume: the constant-volume gas thermometer.
The colour and intensity of radiation from a hot body: pyrometers.
The bending of a bimetallic strip: dial thermometers and thermostats.

A good thermometric property should vary uniformly (steadily) with temperature, over a wide range, and be easy to measure accurately.

Fixed Points and Temperature Scales

To make a temperature scale, choose two reproducible fixed points and divide the interval between them:

The lower fixed point (ice point) is the temperature of pure melting ice at standard atmospheric pressure: 0 °C.
The upper fixed point (steam point) is the temperature of steam above pure water boiling at standard atmospheric pressure: 100 °C.

The fixed interval is 100 degrees on the Celsius scale and 180 degrees on the Fahrenheit scale. The SI unit of temperature is the kelvin (K), on the absolute (thermodynamic) scale, which starts at absolute zero, 0 K = −273.15 °C, the lowest possible temperature.

Converting between scales

T (K) = θ (°C) + 273 (273.15 for precise work)
F = (9/5)C + 32, and C = (5/9)(F − 32)

A change of 1 K equals a change of 1 °C, so temperature differences are the same in both.

Worked example 1

Normal body temperature is 37 °C. Express it in kelvin and in degrees Fahrenheit.

T = 37 + 273 = 310 K. F = (9/5) × 37 + 32 = 66.6 + 32 = 98.6 °F.

Worked example 2

At what temperature do the Celsius and Fahrenheit scales give the same reading?

Set F = C = x: x = (9/5)x + 32, so −(4/5)x = 32, and x = −40. So −40 °C = −40 °F.

Calibrating a Thermometer

If a thermometric property has value X₀ at the ice point and X₁₀₀ at the steam point, and value X(θ) at an unknown temperature, then, assuming the property varies uniformly:

θ = (X(θ) − X₀) ÷ (X₁₀₀ − X₀) × 100 °C

The fraction tells you how far along the fixed interval the reading is.

Worked example 3: a liquid column

The mercury column of an unmarked thermometer is 2.0 cm long in melting ice and 22.0 cm long in steam. What is the temperature when the column is 9.0 cm long?

θ = (9.0 − 2.0) ÷ (22.0 − 2.0) × 100 = 7 ÷ 20 × 100 = 35 °C.

Worked example 4: a resistance thermometer

A platinum wire has a resistance of 4.0 Ω at 0 °C and 5.6 Ω at 100 °C. Its resistance in a liquid is 4.8 Ω. Find the temperature of the liquid.

θ = (4.8 − 4.0) ÷ (5.6 − 4.0) × 100 = 0.8 ÷ 1.6 × 100 = 50 °C.

Worked example 5: a gas thermometer

A constant-volume gas thermometer reads a pressure of 80.0 kPa at the ice point and 109.3 kPa at the steam point. Find the temperature when the pressure is 95.0 kPa.

θ = (95.0 − 80.0) ÷ (109.3 − 80.0) × 100 = 15.0 ÷ 29.3 × 100 ≈ 51.2 °C.

Different thermometric properties do not all vary in exactly the same way with temperature. So two thermometers calibrated at the same fixed points always agree at 0 °C and 100 °C but may give slightly different readings in between. The constant-volume gas thermometer is taken as the standard against which others are checked.

Liquid-in-Glass Thermometers

A thin-walled bulb of liquid is joined to a narrow glass capillary tube. As the temperature rises, the liquid expands far more than the glass, and its thread moves up the tube.

Mercury and alcohol compared

Mercury is opaque and shiny, so it is easy to see. It does not wet (stick to) the glass, expands uniformly, conducts heat well so it responds quickly, and has a wide liquid range, from −39 °C to 357 °C. However, it is poisonous, expensive, and useless for very cold places because it freezes at −39 °C.
Alcohol freezes at −115 °C, so it is suitable for very low temperatures, such as polar weather. It expands about six times more than mercury, giving a more sensitive scale. However, it must be dyed to be visible, it wets the glass, and it boils at 78 °C, so it cannot measure high temperatures.
Water is unsuitable: it has a small range, wets glass, is colourless and, below 4 °C, expands as it cools (its anomalous expansion).

Sensitivity

A thermometer is more sensitive (a small temperature change gives a large movement of the thread) if it has a larger bulb and a narrower bore. It responds more quickly if the bulb has thin glass walls.

The Clinical Thermometer

A clinical thermometer measures human body temperature. Its special features are:

A short range, usually 35 °C to 43 °C, since body temperature never goes far outside it. This allows widely spaced, accurate markings.
A constriction (a narrow kink) in the bore just above the bulb. When the thermometer is removed from the mouth, the mercury below the kink contracts, but the thread above it breaks off and stays in place. The maximum reading can then be read at leisure. The thread is shaken back down before the next use.
A thin-walled bulb for a quick response, and a triangular glass stem that acts as a lens to magnify the thread.

A clinical thermometer must never be sterilised in boiling water: 100 °C is far beyond its range and would burst it. Digital clinical thermometers, using a thermistor whose resistance changes with temperature, have largely replaced mercury ones in hospitals.

Six's Maximum and Minimum Thermometer

Six's thermometer records the highest and lowest temperatures reached since it was last reset, which is useful in weather stations and greenhouses. A U-shaped tube contains mercury in its lower part, with alcohol above it on both sides. One bulb is full of alcohol, and the other is partly empty.

As the temperature rises, the alcohol in the full bulb expands, pushing the mercury round. The mercury pushes a small steel index up the other side, which is left behind at the maximum temperature.
As the temperature falls, the alcohol contracts, and the mercury moves the other way, pushing an index up the first side, where it marks the minimum temperature.
The readings are taken at the bottom ends of the two indexes. They are reset with a magnet, which drags them back down onto the mercury.

Thermocouples

When two different metals, such as copper and iron, are joined at two junctions held at different temperatures, a small e.m.f. is produced. This is the thermoelectric (Seebeck) effect. One junction is kept in melting ice as a reference, and the other is placed where the temperature is to be measured. The e.m.f., read on a sensitive voltmeter, depends on the temperature difference.

Advantages: a very wide range (some types reach about 1500 °C), a tiny junction that responds very quickly and can measure the temperature at a point, and an electrical output that can be read remotely and recorded by computer.
Uses: furnaces, engines, kilns, ovens and industrial processes.

Other Thermometers

Platinum resistance thermometer: the resistance of a platinum coil is measured, often with a Wheatstone bridge. It is very accurate and works over a wide range, but it responds slowly because the coil is fairly large, and it cannot be used for rapidly changing temperatures.
Constant-volume gas thermometer: it measures the pressure of a fixed mass of gas kept at constant volume. It is very accurate over an extremely wide range and is used as the standard, but it is bulky and slow, so it is a laboratory instrument for calibrating other thermometers.
Pyrometer: it measures very high temperatures, such as those of molten metals, from the radiation the hot body emits, without touching it.
Bimetallic thermometer: a coiled strip of two metals with different expansivities bends as the temperature changes, moving a pointer over a dial. The same principle is used in oven and iron thermostats.

Common Mistakes with Temperature and Thermometers

Confusing heat and temperature. Temperature tells you how hot something is. Heat is the energy transferred.
Getting the calibration formula upside down. It is (reading − ice-point value) ÷ (steam-point value − ice-point value) × 100.
Explaining the constriction wrongly. It breaks the thread so that the maximum reading stays in place. It does not stop the mercury expanding.
Choosing mercury for very cold climates. Mercury freezes at −39 °C, so alcohol is used.
Forgetting kelvin is written without a degree sign: 300 K, not 300 °K.

Temperature and Thermometers: Practice Questions

Convert 25 °C to kelvin and to degrees Fahrenheit.
Convert 212 °F to degrees Celsius.
The length of a liquid column is 3.0 cm at 0 °C and 18.0 cm at 100 °C. Find the temperature when the length is 12.0 cm.
A resistance thermometer has resistances of 20.0 Ω at 0 °C and 27.6 Ω at 100 °C. Find its resistance at 40 °C.
State two reasons why mercury is used in thermometers.
Why is a thermocouple suitable for measuring the temperature of a furnace?

Answers: 1. 298 K and (9/5) × 25 + 32 = 77 °F. 2. (5/9) × 180 = 100 °C. 3. (12 − 3) ÷ (18 − 3) × 100 = 9 ÷ 15 × 100 = 60 °C. 4. 20.0 + 0.40 × 7.6 = 23.04 Ω. 5. Any two of: it is opaque and easy to see, it does not wet glass, it expands uniformly, it conducts heat well, and it has a wide range. 6. It has a very wide range, reaching high temperatures, and responds quickly, and its electrical output can be read from a distance.

Conclusion

Temperature measures how hot a body is and decides the direction of heat flow. Thermometers use thermometric properties, such as the length of a liquid column, electrical resistance, thermocouple e.m.f. or gas pressure, calibrated between the ice point (0 °C) and the steam point (100 °C) using θ = (X − X₀)/(X₁₀₀ − X₀) × 100. Mercury and alcohol thermometers suit different ranges, the clinical thermometer uses a constriction and a short range, Six's thermometer records extremes, thermocouples handle high and fast-changing temperatures, and the constant-volume gas thermometer is the standard. Temperatures convert with T = θ + 273 and F = (9/5)C + 32.