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The gas constant occurs in the ideal gas law: = = where P is the absolute pressure, V is the volume of gas, n is the amount of substance, m is the mass, and T is the thermodynamic temperature. R specific is the mass-specific gas constant. The gas constant is expressed in the same unit as molar heat.
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 ...
The ideal gas model has been explored in both the Newtonian dynamics (as in "kinetic theory") and in quantum mechanics (as a "gas in a box"). The ideal gas model has also been used to model the behavior of electrons in a metal (in the Drude model and the free electron model), and it is one of the most important models in statistical mechanics.
Some constants, such as the ideal gas constant, R, do not describe the state of a system, and so are not properties. On the other hand, some constants, such as K f (the freezing point depression constant, or cryoscopic constant ), depend on the identity of a substance, and so may be considered to describe the state of a system, and therefore ...
The standard unit of specific volume is cubic meters per kilogram (m 3 /kg), but other units include ft 3 /lb, ft 3 /slug, or mL/g. [1] Specific volume for an ideal gas is related to the molar gas constant (R) and the gas's temperature (T), pressure (P), and molar mass (M): =
The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas: = = Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is based on the gas constant: R = 8.314 462 618 153 24 m 3 ⋅Pa⋅K −1 ⋅mol −1, or about 8.205 736 608 095 96 × 10 −5 m 3 ⋅atm⋅K ...
where is the isochoric (at constant volume) molar heat capacity of the gas; is constant for an ideal gas. The internal energy of any gas (ideal or not) may be written as a function of the three extensive properties S {\displaystyle S} , V {\displaystyle V} , N {\displaystyle N} (entropy, volume, number of moles ).
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 ...