What is the Meaning of 'w' in an EOS Equation?

[pi.rootpi]

Hey!
The equation of state that connects pressure and energy density is:

$$p=w\rho$$

But what is w?

Thanks!

 

[stevebd1]

Below is an extract from a blog I put together regarding dark energy- 'In cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number w-

$$w=\frac{\text{pressure}}{\text{energy density}}\ \ \ \ \text{or}\ \ \ \ \text{pressure}=w\ \times\ \text{energy density}$$

Energy density per unit volume has the same physical units as pressure and in many circumstances is an exact synonym-

$$\textit{Pressure}\ =\frac{\textit{Force}}{\textit{Area}}=\frac{\textit{F.d}}{\textit{A.d}}=\frac{\textit{W}}{\textit{V}}=\frac{\textit{Energy}}{\textit{Volume}}=\textit{Energy density}$$

where Pressure is in N/m^2, Force is in Newtons, Area in m^2, d is unit of distance (m), W is Work (joules), V is Volume (m^3), Energy is in Joules and Energy density is in joules/m^3

Hence w is dimensionless but is useful in demonstrating the nature of a specific material. For example, ultra-relativistic material such as light has a positive pressure which is equal to 1/3 of the energy density, hence it has an equation of state of w=1/3.

Ultra-relativistic matter, such as radiation, photons, neutrinos and matter from the early universe, w=1/3. For ordinary non-relativistic matter, w=0 (i.e. the pressure is zero). For Quintessence, w<-1/3 (the expansion of the universe is accelerating for any equation of state where w<-1/3). For a cosmological constant, w=-1. Phantom energy is a hypothetical form of dark energy where w<-1, this could cause the expansion of the universe to accelerate so quickly that the big rip would occur.'

 

[sir-pinski]

Hi there!

In an EOS (equation of state), 'w' refers to the parameter known as the equation of state parameter. It is a measure of the relationship between pressure (p) and energy density (ρ) in a given system. This parameter is used to describe the behavior of different types of matter, such as gases, liquids, and solids, under varying conditions of temperature and pressure. The value of 'w' can range from -1 to 1, with different values representing different physical properties of the system. For example, a value of 0 corresponds to a system with no pressure, while a value of 1 represents a system with a constant pressure. The specific meaning of 'w' can vary depending on the context in which it is used, but in general, it is a crucial parameter in understanding the behavior of matter in different environments. I hope this helps clarify things for you!