## 1   Thermodynamic State Variables

Individual particles of a gas have the 'microscopic' properties mass, velocity and momentum. The entire gas, however, is attributed the 'macroscopic' properties volume, pressure, density, temperature, internal energy, enthalpy and entropy. Moreover, the gas consists of a specific number of particles, which can be written as a multiple of the Avogadro constant.

One differentiates between intensive jproperties like temperature and pressure and extensive jproperties like volume, internal energy and particle number. Intensive properties are independent of the size of the ensemble under consideration. Two identical toy balloons taken together do not have double the temperature, but they do have double the volume and double the enthalpy. This should already give pause to anyone wanting to bring the concepts of energy and temperature too close together. One reads in internet forums again and again the assertion that in principle one can measure temperature in the energy units Joules. At the same time it is clear to everyone that you can add energy to a system, without increasing its temperature. It is the clear distinction between these two concepts that lies at the heart of this work.

These macroscopic state variables are constant when the gas is in thermal equilibrium. They are path independent, in that they do not allow any conclusions to be drawn as to how the system got to equilibrium (in phase space).

Process variables jsuch as the work done through expansion or the amount of heat absorbed or emitted, however, are strongly dependent on the path of change. Our investigations will further show how these process variables have to be transformed.

All these state variables are scalar values. We use the usual variable names for all these values. Non-prime capital letters denote values that are measured in the rest frame, i.e. from an observer who is not moving relative to the center of mass of the gas. With primed capital letters we denote the corresponding values that 'fast-moving observers' would ascribe to the gas.