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In this formulation, R * is the gas constant, and the term R * T/Mg gives the scale height (approximately equal to 8.4 km for the troposphere). (For exact results, it should be remembered that atmospheres containing water do not behave as an ideal gas. See real gas or perfect gas or gas for further understanding.)
Using the ideal gas law and the hydrostatic equilibrium equation, gives ¯, which has the solution = (()), where is the gas mass density at the midplane of the disk at a distance r from the center of the star, and is the disk scale height with = ¯ (/ ) (/ ) (/) (¯ / ) , with the solar mass, the astronomical unit, and the atomic mass unit.
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 laws describing the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions are called gas laws.The basic gas laws were discovered by the end of the 18th century when scientists found out that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
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.
h is height from reference point 0, k is the Boltzmann constant, T is the temperature in kelvins. Therefore, instead of pressure being a linear function of height as one might expect from the more simple formula given in the "basic formula" section, it is more accurately represented as an exponential function of height.
In radiosonde observation, the hypsometric equation can be used to compute the height of a pressure level given the height of a reference pressure level and the mean virtual temperature in between. Then, the newly computed height can be used as a new reference level to compute the height of the next level given the mean virtual temperature in ...
This property is usually used by physicists to estimate the height a liquid will rise in a particular capillary tube, radius known, without the need for an experiment. When the characteristic height of the liquid is sufficiently less than the capillary length, then the effect of hydrostatic pressure due to gravity can be neglected. [9]