In this post, I explain the ideal gas law in light of *The UP Hypothesis’ *interpretation of physical reality and identify the nature of its constant *R*. The hypothesis defines the fabric of space as a medium of oscillating massless elements of spherical geometry, referred to as Universal Particles (UPs), which in the absence of mass exist as a continuum under neutral pressure. It defines energy as the motion of those elements, which could be oscillatory, curvilinear or a combination, with temperature as the amplitude of oscillation of UPs. It defines stable matter particles as localized dynamic structures, which develop mass as the exposed background vacuum. The presence of mass alters the pressure distribution in the locality of particles, with mass under negative pressure and the surrounding UPs under positive pressure.

The hypothesis identifies five types of mass, four of which are relevant here— for detailed explanation of those types of mass refer to my post *Types of Mass and The Ultraviolet Catastrophe*. The relevant types of mass are: the gravitational mass, which occupies the centre of any matter particle, the electromagnetic mass or photonic mass, which is generated by the collapse of photons on matter particles, thermal mass, which represents the exposed background vacuum due to the oscillation of the elements of the fabric of space (UPs) and the fourth type is permeability mass, which represents the exposed background vacuum because of the spherical geometry of the elements of the fabric of space.

It should be noted that permeability mass is always constant in any quantum field and as such, it has no effect on any change in the state of matter. And although gravitational mass increases slightly with increased temperature, its increase is negligible and I shall ignore it here. Furthermore, the photonic mass, which is generated by the collapse of photons on matter particles, results in increasing the amplitude of oscillation of the surrounding UPs and is therefore considered as part of the thermal mass. Therefore, only the change in thermal mass is relevant in this brief analysis.

The ideal gas law expresses the relationship between the volume *V*, pressure *P* and absolute temperature *T of an ideal gas *thus,

*PV = nRT *……. (1)

where *n* is the number of moles in the volume of gas and *R* is the ideal gas constant— the subject of this post. Considering one mole of gas, we have:

*R = PV/T *……… (2)

Clearly, a change in any of the variables result in a change in at least one of the other two.

Consider the volume of gas in Fig 1, which shows UPs as small circles and a few gas particles as larger circles. In position (1) the gas is at volume *V*, pressure *P* and temperature *T*, at ambient conditions. If we increase the pressure on the gas particles by lowering the piston (position 2), the particles become agitated, as their charged subatomic particles are forced to a closer proximity. This is manifest as increase in their amplitude of oscillation and results in increased amplitude of the oscillation of the UPs within the volume of gas.

However, unlike matter particles, which are constrained by the cylinder walls and the piston, UPs occupying the space between the atoms are not easily constrained by physical barriers. Therefore, as their amplitude increases, they begin to propagate into the encasement material, causing increase in the amplitudes of the atoms of its walls and subsequently the air particles in the system’s surroundings. The increased amplitude in the container walls and air in surroundings is registered as heat losses.

The reduced density of UPs between gas particles in the cylinder gives those particles more exposed background vacuum (thermal mass) within which they oscillate with greater acceleration. Since each particle has mass, the increased acceleration is translated to increased force of collision between the particles and between them and the container walls, hence the observed increase in pressure. If we were to restrict heat loss by restricting the UPs from existing the container walls, say by using tighter molecular structure, the pressure on the cylinder walls would much greater and may lead to failure of the encasement material.

In position 3, a quantity of heat Q is added to the system. Heat, which is thermal energy, is a function of the amplitude of the oscillation of UPs (temperature). It should be noted that heat could be added to the system by introducing UPs with higher amplitude through the system boundaries by agitating the molecular structure, or by agitating the gas particles by an internal chemical reaction. In any case, increasing the amplitude of UPs leads to reduction in their density and therefore increased force of collision between the gas particles, which registers as further increase in pressure. If this final pressure is greater than that applied to the piston, it results in increase in the volume of the gas, as marked by raised the piston.

Since temperature is the amplitude of oscillation of UPs, it can be considered as a linear spatial dimension. On this basis, if the amplitude of UPs in a gas are unidirectional, say in the x-direction, then temperature could be assigned units of length, e.g. meter (m) instead of Kelvin (K). Thus, the ideal gas constant *R* represent a force (kg. m/s^{2}), as the relationship would become:

*R*** = [ PV /x] (kg. m /s^{2}) ……. (3)**

However, since the increased amplitude of UPs generates thermal mass as exposed background vacuum, it follows that the aggregate effect of the amplitude of UPs is volumetric and may therefore be assigned units of volume. Therefore, instead of assigning arbitrary units in Kelvin K to temperature, we could assign to it the arbitrary units of volume, say cubic meters (m^{3}) and denote the exposed background volume *V _{T}*.

Thus, equation (4.2) above could be rewritten as:

*R*** = [ PV/V_{T}] (N /m^{2}) ……. (4)**

Clearly, the gas constant *R* in equation (4) represents the pressure on one mole of gas. Since mass has a negative pressure, the ideal gas law is saying that increasing the negative pressure around gas particles due to increased thermal mass is compensated for by increase in the force of collision between them and from the surrounding UPs. Thus, the gravitational mass inside the particles and consequently their structural integrity is maintained. However, if cooled, or the pressure on the particles of the gas increases so that the gas changes phase into liquid this law no longer applies, as the cooling process or additional pressure brings the particles closer and restricts their amplitude of oscillation and that of the surrounding UPs. Thus, the temperature of the substance as a liquid is lower.

On account of this interpretation of the gas law, at a specific pressure and temperature, the mass of a specific volume of any gas must be the same regardless of the size of the gas particles, hence Avogadro’s constant, *Na*. This constant confirms the maintained relationship between the gravitational mass and the thermal mass at a specific temperature and pressure. This bring us to Boltzmann constant *k*, which relates the kinetic energy of gas particles to temperature. In terms of the Ideal Gas constant, it is expressed as

*k = R/Na * …….. (5)

Since *Na* is the number of particles in a gas per mole, we can conclude that Boltzmann constant is the pressure distribution around one particle in the gas, because the dimensions of *k* are the same as those of *R* in (4) above, namely N/m^{2}.