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Substituting into the Clapeyron equation =, we can obtain the Clausius–Clapeyron equation [8]: 509 = for low temperatures and pressures, [8]: 509 where is the specific latent heat of the substance. Instead of the specific, corresponding molar values (i.e. L {\displaystyle L} in kJ/mol and R = 8.31 J/(mol⋅K)) may also be used.
where ln denotes the natural logarithm, is the thermodynamic equilibrium constant, and R is the ideal gas constant.This equation is exact at any one temperature and all pressures, derived from the requirement that the Gibbs free energy of reaction be stationary in a state of chemical equilibrium.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
R ∗ = 8.314 32 × 10 3 N⋅m⋅kmol −1 ⋅K −1 = 8.314 32 J⋅K −1 ⋅mol −1. Note the use of the kilomole, with the resulting factor of 1000 in the constant. The USSA1976 acknowledges that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant. [ 13 ]
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.. Historically, thermodynamic temperature was defined by Lord Kelvin in terms of a macroscopic relation between thermodynamic work and heat transfer as defined in thermodynamics, but the kelvin was redefined by international agreement in 2019 in terms of phenomena that are ...
The state of a simple compressible system is completely specified by two independent, intensive properties [2] A more general statement of the state postulate says: the state of a simple system is completely specified by r+1 independent, intensive properties where r is the number of significant work interactions. [1] [3]
The thermodynamic equation for the Gibbs energy change accompanying mixing at constant temperature and (external) pressure is = A change, denoted by , is the value of a variable for a solution or mixture minus the values for the pure components considered separately.
In 1842 Clapeyron published his findings on the "optimal position for the piston at which the various valves should be opened or closed." [1] [4] In 1843, Clapeyron further developed the idea of a reversible process, already suggested by Carnot and made a definitive statement of Carnot's principle, what is now known as the second law of ...