Describing a gas: pressure, volume, temperature

The state of a gas enclosed in a container is described by four quantities, its state variables:

   P  : pressure            (in pascals, Pa)      -> force of impacts on the walls
   V  : volume              (in cubic metres, m³) -> the space occupied
   T  : temperature         (in KELVINS, K)       -> the agitation of the molecules
   n  : amount of substance (in moles, mol)       -> the number of molecules

One crucial point from the start: temperature must be expressed in kelvins, never in degrees Celsius. The Kelvin scale starts from absolute zero (−273.15 °C), the temperature where agitation ceases. You convert between the two by:

   T(K) = θ(°C) + 273.15

Why is this vital? Because the gas laws involve ratios and products of temperature. Using degrees Celsius (which can be negative and whose zero is arbitrary) would give absurd results. In kelvins, T is always positive and proportional to the real agitation.

These four quantities are not independent: if you fix some, the others are constrained. Compress a gas (V decreases) and its pressure rises; heat it (T increases) and it pushes harder on the walls. The whole point is to find the exact relation that binds them. Physicists first discovered it piece by piece, fixing two quantities and observing the other two — the subject of the next lesson.