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The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant , expressed in units of energy per temperature increment per amount of substance , rather than energy per temperature increment per particle .
p is the gas pressure; R is the gas constant, T is temperature, V m is the molar volume (V/n), a is a constant that corrects for attractive potential of molecules, and; b is a constant that corrects for volume. The constants are different depending on which gas is being analyzed. The constants can be calculated from the critical point data of ...
Arrhenius originally considered A to be a temperature-independent constant for each chemical reaction. [6] However more recent treatments include some temperature dependence – see § Modified Arrhenius equation below. E a is the molar activation energy for the reaction, R is the universal gas constant. [1] [2] [4]
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 .
A is the first virial coefficient, which has a constant value of 1 and makes the statement that when volume is large, all fluids behave like ideal gases. The second virial coefficient B corresponds to interactions between pairs of molecules, C to triplets, and so on.
where R is the ideal gas constant. According to Mayer's relation, the molar heat capacity at constant pressure would be c P,m = c V,m + R = 1 / 2 fR + R = 1 / 2 (f + 2)R. 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).
The heat that is added to the gas goes only partly into heating the gas, while the rest is transformed into the mechanical work performed by the piston. In the first, constant-volume case (locked piston), there is no external motion, and thus no mechanical work is done on the atmosphere; C V is used. In the second case, additional work is done ...
The van der Waals equation of state may be written as (+) =where is the absolute temperature, is the pressure, is the molar volume and is the universal gas constant.Note that = /, where is the volume, and = /, where is the number of moles, is the number of particles, and is the Avogadro constant.