page_title: Temperature
section_title: Kinetic theory of gases
hierarchical_section_title: Temperature / Theoretical foundation / Kinetic theory of gases
caption_attribution_description: English: Plots of pressure vs temperature for three different gas samples at the same volume extrapolate to absolute zero.
context_page_description: Temperature is a physical property of matter that quantitatively expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, when a body is in contact with another that is colder.
  Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have used various reference points and thermometric substances for definition. The most common scales are the Celsius scale, the Fahrenheit scale, and the Kelvin scale, the last of which is predominantly used for scientific purposes by conventions of the International System of Units.
  The lowest theoretical temperature is absolute zero, at which no more thermal energy can be extracted from a body. Experimentally, it can only be approached very closely, but not reached, which is recognized in the third law of thermodynamics.
  Temperature is important in all fields of natural science, including physics, chemistry, Earth science, medicine, biology, ecology and geography as well as most aspects of daily life.
context_section_description: Maxwell and Boltzmann developed a kinetic theory that yields a fundamental understanding of temperature in gases.
  This theory also explains the ideal gas law and the observed heat capacity of monatomic  (or 'noble') gases.
  The ideal gas law is based on observed empirical relationships between pressure (p), volume (V), and temperature (T), and was recognized long before the kinetic theory of gases was developed (see Boyle's and Charles's laws).  The ideal gas law states:
  where n is the number of moles of gas and R = 8.314462618... J⋅mol⁻¹⋅K⁻¹  is the gas constant.
  This relationship gives us our first hint that there is an absolute zero on the temperature scale, because it only holds if the temperature is measured on an absolute scale such as Kelvin's. The ideal gas law allows one to measure temperature on this absolute scale using the gas thermometer.  The temperature in kelvins can be defined as the pressure in pascals of one mole of gas in a container of one cubic meter, divided by the gas constant.
  Although it is not a particularly convenient device, the gas thermometer provides an essential theoretical basis by which all thermometers can be calibrated.  As a practical matter, it is not possible to use a gas thermometer to measure absolute zero temperature since the gases tend to condense into a liquid long before the temperature reaches zero. It is possible, however, to extrapolate to absolute zero by using the ideal gas law, as shown in the figure.
  The kinetic theory assumes that pressure is caused by the force associated with individual atoms striking the walls, and that all energy is translational kinetic energy.  Using a sophisticated symmetry argument, Boltzmann deduced what is now called the Maxwell–Boltzmann probability distribution function for the velocity of particles in an ideal gas.  From that probability distribution function, the average kinetic energy (per particle) of a monatomic ideal gas is
  where the Boltzmann constant kB is the ideal gas constant divided by the Avogadro number, and  is the root-mean-square speed. Thus the ideal gas law states that internal energy is directly proportional to temperature. This direct proportionality between temperature and internal energy is a special case of the equipartition theorem, and holds only in the classical limit of an ideal gas. It does not hold for most substances, although it is true that temperature is a monotonic (non-decreasing) function of internal energy.
caption: Plots of pressure vs temperature for three different gas samples extrapolated to absolute zero
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