Momentum work and the energetic foundations of physics. II. The ideal gas law derived via processes

In Paper I of this series, the elastic collision was described via simultaneous processes, where the energy is conserved at any moment. In this paper, we critically review the kinetic theory of gases, which was developed based on Newtonian mechanics, and show that it violates the principle of the conservation of energy. By placing the energy conservation at the beginning of the deductive formalism, we derive the ideal gas law via equally strong simultaneous counter-processes at the walls, namely, momentum work and volume work. Several new insights into the state variables of an ideal gas are obtained: (i) pressure cannot be expressed via the kinetic energy of an ideal gas, and (ii) temperature can be interpreted as a particle-related (microscopic) state variable. The historical choice to set a zero point of the potential energy for a confined ideal gas needs to be corrected, and the internal energy of an ideal gas turns out to include more forms of energy than specified in the kinetic theory of gases. Finally, and importantly, we show that the process approach to an ideal gas and thus to collisions is experimentally confirmed.