The ideal gas law

The ideal gas model treats a gas as a collection of tiny particles and rests on four key assumptions:

• A gas consists of a large number of tiny atoms in rapid, random motion
• The individual volumes of the atoms are negligible compared with the volume of the container
• Collisions between the atoms (and with the container walls) are perfectly elastic
• No forces act between the atoms except during those brief collisions

These four assumptions strip away the complexity of real molecular interactions, leaving a system whose internal energy is entirely kinetic and depends only on temperature.

The equation

PV = nRT = Nk_BT

connects the macroscopic state variables — pressure, volume, temperature, and amount of gas — into a single relationship. This equation reveals three core proportionalities:

• Pressure is inversely proportional to volume at constant temperature (Boyle's law)
• Pressure is directly proportional to absolute temperature when volume is held constant (the pressure law)
• Volume is directly proportional to absolute temperature when pressure is held constant (Charles's law)

Graphs of these relationships confirm the proportionalities and, through extrapolation of a pressure–temperature graph in Celsius, identify absolute zero at

-273 °C

Mastering unit conversion to kelvin and pascals is essential, because a single unconverted value invalidates the entire calculation.