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ZealScience said:Also what is meant by your 'derivation'? The first few lines seem to be Boyle's Law and similar which is empirical. If you mean deriving from statistical mechanics and kinetic gas theory, I expect more algebra though.
The ideal gas equation, also known as the ideal gas law, is a mathematical relationship between the four variables that describe the behavior of an ideal gas: pressure (P), volume (V), temperature (T), and moles of gas (n). It is written as PV = nRT, where R is the universal gas constant.
The ideal gas equation can be derived from combining the three gas laws: Boyle's Law, Charles's Law, and Avogadro's Law. Boyle's Law states that at a constant temperature, the product of pressure and volume is constant. Charles's Law states that at a constant pressure, the volume of a gas is directly proportional to its temperature. And Avogadro's Law states that at a constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas. By combining these laws, we can arrive at the ideal gas equation.
The ideal gas equation is based on several assumptions, including that the gas particles have no volume and do not interact with each other, and that there are no intermolecular forces present. Additionally, the ideal gas equation assumes that the gas is at a low enough pressure and high enough temperature that it behaves like an ideal gas.
The units used in the ideal gas equation depend on the units used for the variables in the equation. Typically, pressure is measured in atmospheres (atm), volume in liters (L), temperature in Kelvin (K), and moles in moles (mol). However, other units such as pascals (Pa), cubic meters (m^3), and kelvin (°C) can also be used, as long as they are consistent throughout the equation.
The ideal gas equation is used to predict the behavior of gases in various real-world applications, such as in the design of gas storage tanks, the production of industrial gases, and the study of atmospheric gases. It is also used in the ideal gas law calculator to solve for any of the variables in the equation, given the values of the others.