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As a rule of thumb, the ideal gas law is reasonably accurate up to a pressure of about 2 atm, and even higher for small non-associating molecules. For example, methyl chloride , a highly polar molecule and therefore with significant intermolecular forces, the experimental value for the compressibility factor is Z = 0.9152 {\displaystyle Z=0. ...
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 ...
In the case of an ideal gas, the compressibility factor Z is equal to unity, and the familiar ideal gas law is recovered: p = R T V m {\displaystyle p={\frac {RT}{V_{m}}}} Z can, in general, be either greater or less than unity for a real gas.
Below are useful results from the Maxwell–Boltzmann distribution for an ideal gas, and the implications of the Entropy quantity. The distribution is valid for atoms or molecules constituting ideal gases.
At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures.
The ideal gas law is the equation of state for an ideal gas, given by: = where P is the pressure; V is the volume; n is the amount of substance of the gas (in moles) T is the absolute temperature; R is the gas constant, which must be expressed in units consistent with those chosen for pressure, volume and temperature.
Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure p and volume V is proportional to the product of amount of substance n and absolute temperature T: =, where R is the molar gas constant (8.314 462 618 153 24 J⋅K −1 ⋅mol −1). [4]
For an ideal gas, the ideal gas law applies without restrictions on the specific heat. An ideal gas is a simplified "real gas" with the assumption that the compressibility factor Z is set to 1 meaning that this pneumatic ratio remains constant. A compressibility factor of one also requires the four state variables to follow the ideal gas law.