# What is w in a EOS?

1. Dec 26, 2008

### pi.rootpi

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

$$p=w\rho$$

But what is w???

Thanks!

2. Dec 27, 2008

### 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.'

Last edited: Dec 28, 2008