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Under these conditions, p 1 V 1 γ = p 2 V 2 γ, where γ is defined as the heat capacity ratio, which is constant for a calorifically perfect gas. The value used for γ is typically 1.4 for diatomic gases like nitrogen (N 2) and oxygen (O 2), (and air, which is 99% diatomic).
v = velocity of atom/molecule, m = mass of each molecule (all molecules are identical in kinetic theory), γ(p) = Lorentz factor as function of momentum (see below) Ratio of thermal to rest mass-energy of each molecule: = /
In physics, the thermal equation of state is a mathematical expression of pressure P, temperature T, and, volume V.The thermal equation of state for ideal gases is the ideal gas law, expressed as PV=nRT (where R is the gas constant and n the amount of substance), while the thermal equation of state for solids is expressed as:
where P is the pressure, V is the volume, N is the number of gas molecules, k B is the Boltzmann constant (1.381×10 −23 J·K −1 in SI units) and T is the absolute temperature. These equations are exact only for an ideal gas , which neglects various intermolecular effects (see real gas ).
where c p is the specific heat capacity for a constant pressure and c v is the specific heat capacity for a constant volume. [9] It is common, especially in engineering applications, to represent the specific gas constant by the symbol R. In such cases, the universal gas constant is usually given a different symbol such as R to distinguish it ...
It is an intermediate mathematical model, useful as a pedagogical tool when teaching physics, chemistry, and engineering. In addition, its saturation curve has an analytic solution, which can depict the liquid metals (mercury and cesium) quantitatively, and describes most real fluids qualitatively. [ 25 ]
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. [1] [2] Most modern equations of state are formulated in the Helmholtz free energy.
Here, U is internal energy, T is absolute temperature, S is entropy, P is pressure, and V is volume. This is only one expression of the fundamental thermodynamic relation. It may be expressed in other ways, using different variables (e.g. using thermodynamic potentials). For example, the fundamental relation may be expressed in terms of the ...