The inversion temperature in
thermodynamics
Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
and
cryogenics
In physics, cryogenics is the production and behaviour of materials at very low temperatures.
The 13th International Institute of Refrigeration's (IIR) International Congress of Refrigeration (held in Washington, DC in 1971) endorsed a universa ...
is the critical temperature below which a non-
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...
(all gases in reality) that is expanding at constant
enthalpy will experience a temperature decrease, and above which will experience a temperature increase. This temperature change is known as the
Joule–Thomson effect, and is exploited in the
liquefaction of gases. Inversion temperature depends on the nature of the gas.
For a
van der Waals gas we can calculate the
enthalpy using
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
as
:
where
is the number of molecules,
is volume,
is temperature (in the
Kelvin scale),
is the
Boltzmann constant, and
and
are constants depending on intermolecular forces and molecular volume, respectively.
From this equation, if enthalpy is kept constant and there is an increase of volume, temperature must change depending on the sign of
. Therefore, our inversion temperature is given where the sign flips at zero, or
:
,
where
is the
critical temperature
Critical or Critically may refer to:
*Critical, or critical but stable, medical states
**Critical, or intensive care medicine
*Critical juncture, a discontinuous change studied in the social sciences.
*Critical Software, a company specializing in ...
of the substance. So for
, an expansion at constant enthalpy increases temperature as the
work done by the repulsive interactions of the gas is dominant, and so the change in kinetic
energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
is positive. But for
, expansion causes temperature to decrease because the work of attractive intermolecular forces dominates, giving a negative change in average molecular speed, and therefore kinetic energy.
See also
*
Critical point (thermodynamics)
In thermodynamics, a critical point (or critical state) is the end point of a phase Equilibrium (thermodynamics), equilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designat ...
*
Phase transition
In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic Sta ...
*
Joule–Thomson effect
References
{{reflist
External links
Thermodynamic Concepts and Processes (Chapter 2)(part of the Statistical and Thermal Physics (STP) Curriculum Development Project at
Clark University)
Temperature
Thermodynamic properties
Engineering thermodynamics
Industrial gases
Gases