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The classical equipartition theorem predicts that the heat capacity ratio (γ) for an ideal gas can be related to the thermally accessible degrees of freedom (f) of a molecule by = +, =. Thus we observe that for a monatomic gas, with 3 translational degrees of freedom per atom: γ = 5 3 = 1.6666 … , {\displaystyle \gamma ={\frac {5}{3}}=1. ...
Most materials have Poisson's ratio values ranging between 0.0 and 0.5. For soft materials, [1] such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson's ratio is near 0.5. For open-cell polymer foams, Poisson's ratio is near zero, since the cells tend to collapse in compression.
Note that the especially high molar values, as for paraffin, gasoline, water and ammonia, result from calculating specific heats in terms of moles of molecules. If specific heat is expressed per mole of atoms for these substances, none of the constant-volume values exceed, to any large extent, the theoretical Dulong–Petit limit of 25 J⋅mol ...
The only possible motion of an atom in a monatomic gas is translation (electronic excitation is not important at room temperature). Thus by the equipartition theorem , the kinetic energy of a single atom of a monatomic gas at thermodynamic temperature T is given by 3 2 k B T {\displaystyle {\frac {3}{2}}k_{\text{B}}T} , where k B is the ...
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Thus, each additional degree of freedom will contribute 1 / 2 R to the molar heat capacity of the gas (both c V,m and c P,m). In particular, each molecule of a monatomic gas has only f = 3 degrees of freedom, namely the components of its velocity vector; therefore c V,m = 3 / 2 R and c P,m = 5 / 2 R. [10]
In transition regions, where this pressure dependent dissociation is incomplete, both beta (the volume/pressure differential ratio) and the differential, constant pressure heat capacity greatly increases. For moderate pressures, above 10,000 K the gas further dissociates into free electrons and ions.
The van der Waals equation is a mathematical formula that describes the behavior of real gases.It is an equation of state that relates the pressure, temperature, and molar volume in a fluid.