# Temperature

In everyday terms, temperature is a measure of the "hotness" or "coldness" of a substance. More technically, temperature indicates the direction in which energy flows (as heat) when two objects are in thermal contact: energy flows as heat from a high temperature region to a low temperature region. In other words, temperature is simply an indicator of the expected direction of flow of energy as heat.

Temperature is not heat. Heat is energy in transition; temperature is the signpost of the expected direction of that transition. A large quantity of energy can flow as heat from one region to another even though the temperature difference between the regions is minute.

Temperature is not energy. A very large, cold block of metal will have a low temperature but may contain a very large amount of energy. A small block of the same material having the same temperature will contain less energy. This distinction is expressed by saying that temperature is an intensive property, a property independent of the size of the sample; whereas energy content is an extensive property, a property that does depend on the size of the sample. Thus, a sample taken from a tank of hot water will have the same temperature regardless of the size of the sample, but the energy content (more formally, the internal energy) of a large sample is greater than that of a small sample.

At a molecular level, the temperature of a system indicates the distribution of "populations" of energy levels within the system: the higher the temperature, the greater the proportion of molecules in a state of high energy. If the numbers of molecules in two energy states, separated by an energy difference Δ E, are N upper and N lower , then the temperature is

T = (Δ E / k ) ln( N lower / N upper )   (1)

where k is Boltzmann's constant, a fundamental constant of nature. We see that the greater the ratio N lower / N upper for a given energy difference, the higher the temperature. This molecular interpretation has a special significance in cases in which the only contribution to the overall energy is kinetic energy, which is the case in a perfect (ideal) gas. In that case, high temperature corresponds to a higher average speed of the molecules and a wider range of speeds in the sample. The average speed c of molecules of mass m at a temperature T is

c = (8 kT / π m ) ½    (2)

and so the average speed increases with the square root of the temperature.

Temperature is measured with a thermometer, a device in which a physical property of some component of the device changes when the device is put in thermal contact with a sample. That property may be the volume of a liquid (as in a mercury-in-glass thermometer) or an electrical property such as resistance. Electronic probes based on resistance changes in a semiconductor material are also used to measure temperature.

Three scales of temperature are still commonly encountered. The Fahrenheit scale is used in the United States for domestic purposes. On this A woman is checking a baby's temperature. A high temperature indicates more energy in the body and possibly an illness.

scale, the freezing point of water is 32°F and its boiling point is 212°F. This scale has been discarded by virtually all other countries in favor of the Celsius scale, which is used for all scientific work. On the Celsius scale, the freezing point of water corresponds to 0°C and the boiling point corresponds to 100°C. A more fundamental scale is the Kelvin scale, which sets 0 at the absolute zero of temperature (corresponding to −273.15°C), and adopts a scale in which the triple point of water (the temperature at which ice, water, and water vapor coexist at equilibrium ) is exactly 273.16 K. This scale ensures that the magnitude of the kelvin (as the unit for the Kelvin scale is called) is the same as that of the Celsius degree.

The Kelvin scale is used to express the thermodynamic temperature, denoted T, with T = 0 as the lowest possible temperature (when all motion has ceased). Temperatures on the Celsius and Fahrenheit scales are denoted θ (theta). Two important conversions are:

θ /ºC = 5 / 9 ( θ /ºF −32)   (3)

T / K = θ /ºC + 273.15   (4)

In chemistry, it is often necessary to keep a system at a constant temperature, for otherwise observations and measurements would provide a reading that was an average of a temperature-dependent property, such as reaction rate. One way to achieve a constant temperature is to immerse the system in a water bath containing a large volume of water, the temperature of which is controlled by a heater and a thermostat. A thermostat is a device for switching a current on and off according to whether the temperature of the system is above or below a selected value. It incorporates a temperature probe (a thermometer with an electric output) and electronic devices for interpreting the temperature and effecting the switching. The same principle is the basis of the thermostat that is used in homes.

The chemical effects of greater temperature include changes in the rate of reaction and the position of chemical equilibrium. Almost all reactions proceed more rapidly at higher temperatures because the molecules (in the gas phase ) collide more vigorously at higher temperatures. A thermodynamic consequence of changing temperature is that the equilibrium constant of an exothermic reaction decreases as the temperature is raised, so reactants are more favored at low temperatures than at high. This dependence is sometimes referred to as Le Chatelier's principle, but it is better to regard it as a consequence of thermodynamics and in particular of the second law of thermodynamics.

Although T = 0 is the lowest attainable temperature, it is possible to achieve negative temperatures. This seemingly paradoxical remark is resolved as follows. When a system has only two energy levels, all finite temperatures correspond to a distribution of populations in which more molecules occupy the lower state than the upper. However, it is possible by artificial means to invert the populations, so that briefly there would be more molecules in the upper state than the lower. It follows from equation 1 that T is then negative.

The thermodynamic justification for introducing the temperature into science is the Zeroth Law, which states that if system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then A and C would also be in thermal equilibrium with each other, if they were put in contact. The third law of thermodynamics is also relevant here: it states that absolute zero ( T = 0) is not attainable in a finite number of steps.

Peter Atkins

## Bibliography

Atkins, Peter, and de Paula, Julio (2002). Atkins' Physical Chemistry, 7th edition. New York: Oxford University Press.

Smith, Crosbie (1998). The Science of Energy: A Cultural History of Energy Physics in Victorian Britain. Chicago: University of Chicago Press.

Tipler, Paul A. (1999). Physics for Scientists and Engineers, 4th edition. New York: W. H. Freeman; Worth Publishers.