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The thermodynamic square (also known as the thermodynamic wheel, Guggenheim scheme or Born square) is a mnemonic diagram attributed to Max Born and used to help determine thermodynamic relations. Born presented the thermodynamic square in a 1929 lecture. [1] The symmetry of thermodynamics appears in a paper by F.O. Koenig. [2]
In statistical physics and thermodynamics, the Maxwell construction is a method for addressing the physically unrealistic aspects of certain models of phase transitions. Named for physicist James Clerk Maxwell , it considers areas of regions on phase diagrams .
Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell .
Mathematically, the Maxwell–Boltzmann distribution is the chi distribution with three degrees of freedom (the components of the velocity vector in Euclidean space), with a scale parameter measuring speeds in units proportional to the square root of / (the ratio of temperature and particle mass). [2]
Diagram of thermodynamic surface from Maxwell's book Theory of Heat.The diagram is drawn roughly from the same angle as the upper left photo above, and shows the 3D axes e (energy, increasing downwards), ϕ (entropy, increasing to the lower right and out-of-plane), and v (volume, increasing to the upper right and into-plane).
Maxwell relations in thermodynamics are often used to derive thermodynamic relations. [ 2 ] The Clapeyron equation allows us to use pressure, temperature, and specific volume to determine an enthalpy change that is connected to a phase change.
With a model of the microscopic constituents of a system, one can calculate the microstate energies, and thus the partition function, which will then allow us to calculate all the other thermodynamic properties of the system. The partition function can be related to thermodynamic properties because it has a very important statistical meaning.
Maxwell–Boltzmann statistics is used to derive the Maxwell–Boltzmann distribution of an ideal gas. However, it can also be used to extend that distribution to particles with a different energy–momentum relation, such as relativistic particles (resulting in Maxwell–Jüttner distribution), and to other than three-dimensional spaces.