Temperature

Fields of Study: Fields of Study: Algebra; Measurement.

Summary: Scientists and mathematicians have developed and investigated a variety of principles and scales associated with the measurement and definition of temperature.

Quantification of temperature is necessary for many reasons, including scientific experiments, weather prediction, and many manufacturing processes. Temperature, by its formal definition, measures the movement of molecules in an object. Greater movement results in higher temperatures; conversely, less movement results in lower temperatures. The byproduct is heat, so temperature is often thought to measure the heat of an object. Mathematicians, many of whom are also physicists, have made significant contributions in quantifying heat and developing the temperature scales widely used in the twenty-first century.

History

Joseph Fourier began heat investigations in the early nineteenth century. His work On the Propagation of Heat in Solid Bodies was controversial at the time of its publication in 1807. Joseph Lagrange and Pierre-Simon Laplace argued against Fourier’s trigonometric series expansions; however, Fourier series are widely used in a variety of theories and applications in the twenty-first century. Jean-Baptiste Biot, Simone Poisson, and Laplace objected at various times to Fourier’s derivation of his heat transfer equations. In 1831, Franz Neumann formulated the notion that molecular heat is the sum of the atomic heats of the components. Studying mixtures of hot and cold water, which did not produce water that was the average of the two temperatures, he concluded that water’s specific gravity increases with temperature. This relationship was later shown by other researchers to be true only for a certain range of temperatures. In the late nineteenth century, James Maxwell and Ludwig Boltzmann independently developed what is now known as the “Maxwell–Boltzmann kinetic theory of gases,” showing that heat is a function of only molecular movement. Their equations have many applications, including estimating the heat of the sun.

Around the same time, Josef Stefan proposed that the total energy emitted by a hot body was proportional to the fourth power of the temperature, based on empirical observations. In the twentieth and twenty-first centuries, scientists continued to study heat and have developed mathematical and statistical models to estimate heat. These models are used in areas like astronomy, weather prediction, and the global warming debate.

Measuring Tools and Temperature Scales

Heat can be difficult to quantify. Scientists and mathematicians developed many methods and instruments to measure and describe perceived temperature. Some of the earliest were called thermoscopes, often attributed to Galileo Galilei. In the early 1700s, Gabriel Fahrenheit created mercury thermometers and marked them with units that became known as “degrees Fahrenheit.” He empirically calibrated his thermometer using three values. Icy salt water was assigned temperature zero. Pure ice water was labeled 30. A healthy man would show a reading of 96 degrees Fahrenheit. Later, Fahrenheit would measure the temperature of pure boiling water as 212 degrees Fahrenheit, adjusting the freezing point of water to be 32 degrees Fahrenheit so there was 180 degrees between the freezing and boiling point of water.

Anders Celsius created a different temperature scale in the mid-1700s. The Celsius temperature scale was numerically inverted with respect to Fahrenheit. He used 100 to indicate the freezing point of water and 0 for the boiling point of water. Because there were 100 steps in his temperature scale, he referred to it as a “centigrade” (centi means “a hundred” and grade means “step”). A few years later, Carolus Linnæus allegedly reversed the scale to make zero the freezing point and 100 the boiling point.

About a century after Celsius created his scale, William Thomson, Lord Kelvin, is given credit for the idea of an absolute zero, a temperature so cold that molecules do not move. The Kelvin scale was precisely defined much later after scientists and mathematicians better understood the concept of conservation of energy. Near-absolute zero conditions produce many interesting problems in mathematics and science. For example, clumping of atoms as they approach an unmoving state can be studied as a classic packing problem, which has extensions in areas like materials science and digital compression. The Kelvin temperature scale uses the same scale as centigrade, with absolute zero about 273 degrees below the freezing point of pure water. Converting from degrees centigrade to Kelvin is as simple as shifting the scale by adding 273.

In the mid-twentieth century, the centigrade scale was replaced with the Celsius scale. The changes were relatively minor, so one estimates the freezing and boiling points of water to be 0 degrees Celsius and 100 degrees Celsius. In actuality, 100 degrees Celsius (the boiling point of water) is now 99.975 degrees Celsius. Converting from degrees Celsius to degrees Fahrenheit, or degrees Fahrenheit to degrees Celsius, involves multiplicative rescaling, not just translation, since 1 degree Celsius is 1.8 times larger than 1 degree Fahrenheit.

Bibliography

Callen, Herbert B. Thermodynamics and an Introduction to Thermostatistics. Wiley, 1985.

Chang, Hasok. Inventing Temperature: Measurement and Scientific Progress. Oxford UP, 2004.

Lipták, Béla G. Temperature Measurement. Chilton Book, 1993.

Pitts, Donald R., and Leighton E. Sissom. Schaum’s Outline of Theory and Problems of Heat Transfer. McGraw-Hill, 1998.

Quinn, T. J. Temperature. Academic Press, 1990.

Zimmerman, Kim Ann. "Temperature: Facts, History & Definition." Live Science, 20 Sept. 2013, www.livescience.com/39841-temperature.html. Accessed 22 Feb. 2017.