# Ideal gas law

The ideal gas law or equation is the equation of state of an ideal gas. It combines the three primitive gas laws derived from early physics researchers. Although roughly accurate for gases at low pressures and high temperatures, it becomes increasingly inaccurate at higher pressures and lower temperatures. The equation has the form:

[itex]P = {RT\over{\tilde{V}}}[itex]

where P is the pressure of an ideal gas, T is its temperature, and [itex]\tilde{V}[itex] is its molar volume.

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Isoth.png
Some isotherms of an ideal gas (i.e. the relation between pressure P and volume V at fixed temperature T; plotted for a set of temperatures, with increasing T from lower to upper curve)

Using statistical mechanics, the ideal gas law can be derived by assuming that a gas is composed of a large number of small molecules, with no attractive or repulsive forces. In reality, gas molecules do interact with attractive and repulsive forces. In fact it is these forces that result in the formation of liquids.

The ideal gas law is often used as a very rough approximation in science and engineering calculations for the behavior of a real diffuse gas. Though often highly inaccurate, the equation is very simple, making it easy to obtain straightforward solutions to a number of physics and engineering problems that otherwise would require complicated numerical methods of computation. More complicated equations of state, such as the Peng-Robinson or Van der Waals equation, are significantly more accurate, however, they are cubic equations which, when solved, may result in multiple roots. The existence of multiple roots is necessary in order for the equation of state to predict the existence of multiple phases, such as the gas and liquid phase. Because the ideal gas law is not cubic, however, it fails to predict condensation from a gas to a liquid.

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