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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.
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 ...
Real gases are non-ideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behaviour of real gases, the following must be taken into account: compressibility effects; variable specific heat capacity; van der Waals forces; non-equilibrium thermodynamic effects;
which is the ideal gas law. [22] This is not surprising since the van der Waals equation was constructed from the ideal gas equation in order to obtain an equation valid beyond the limit of ideal gas behavior. What is truly remarkable is the extent to which van der Waals succeeded.
This is the virial equation of state and describes a real gas. Since higher order virial coefficients are generally much smaller than the second coefficient, the gas tends to behave as an ideal gas over a wider range of pressures when the temperature reaches the Boyle temperature (or when c = 1 V m {\textstyle c={\frac {1}{V_{m}}}} or P ...
Thus water behaves as though it is an ideal gas that is already under about 20,000 atmospheres (2 GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100 kPa to 200 kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002 ...
Under these conditions, air behaves only approximately as an ideal gas. As a result, the real temperature change will not be exactly zero. Rather, one can calculate that the temperature of the air should drop by about 3 degrees Celsius when the volume is doubled under adiabatic conditions. [ 12 ]
Note from these that (/) (/) =; the van der Waals saturated vapor is an ideal gas in this limit. To paraphrase Sommerfeld, it is remarkable that the theory due to van der Waals is able to predict that when s g − s f ≫ 2 R {\displaystyle s_{g}-s_{f}\gg 2R} the saturated vapor behaves like an ideal gas; the saturated vapor of real gases ...