Short answers, pulled from the story.
The word gas was first used by the early 17th-century Brabantian or Southern Netherlandish chemist Jan Baptist van Helmont. It appears to be a phonetic transcription of the Ancient Greek word chaos, following an alchemical usage first attested in the works of Paracelsus. Van Helmont also identified carbon dioxide, the first known gas other than air.
The ideal gas law reads PV equals nRT, where P is pressure, V is volume, n is the amount of gas in moles, R is the universal gas constant of 8.314 joules per mole-kelvin, and T is temperature. This form is sometimes called the chemist's version because it emphasizes the number of molecules n. An ideal gas is a simplified real gas with a compressibility factor Z set to one.
Boyle's law states that at constant temperature, the pressure of a gas varies inversely with its volume, so the product of pressure and volume stays constant. In 1662 Robert Boyle discovered it using a J-shaped glass tube sealed at one end, trapping air with mercury and measuring volume as he added more mercury. If the volume is halved, the pressure is doubled.
Gases are described through four physical properties: pressure, volume, number of particles, and temperature. Chemists group the number of particles in units called moles. These four characteristics were repeatedly observed by scientists including Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac, and Amedeo Avogadro.
The primary difference is intermolecular forces, especially van der Waals forces, which a real gas experiences but an ideal gas ignores. At low temperatures and low pressures a real gas occupies less volume than the ideal gas law predicts, while at high temperatures and high pressures it occupies more. Ignoring these proximity-dependent forces allows a real gas to be treated like an ideal gas, which greatly simplifies calculation.
A permanent gas is a gas with a critical temperature below the range of normal human-habitable temperatures, so it cannot be liquefied by pressure within that range. Historically such gases were thought impossible to liquefy and to remain permanently in the gaseous state. The term is relevant to ambient temperature storage and transport of gases at high pressure.