Equation of State in the Presence of Gravity
arXiv:1608.03409 · doi:10.3938/jkps.69.1597
Abstract
We investigate how an equation of state for matter is affected when a gravity is present. For this purpose, we consider a box of ideal gas in the presence of Newtonian gravity. In addition to the ordinary thermodynamic quantities, a characteristic variable that represents a weight per unit area relative to the average pressure is required in order to describe a macroscopic state of the gas. Although the density and the pressure are not uniform due to the presence of gravity, the ideal gas law itself is satisfied for the thermodynamic quantities when averaged over the system. Assuming that the system follows an adiabatic process further, we obtain a {\it new} relation between the averaged pressure and density, which differs from the conventional equation of state for the ideal gas in the absence of gravity. Applying our results to a small volume in a Newtonian star, however, we find that the conventional one is reliable for most astrophysical situations when the characteristic scale is small. On the other hand, gravity effects become significant near the surface of a Newtonian star.
7 pages, no figure, minor corrections
References in corpus (6)
- Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
- Palatini Approach to Modified Gravity: f(R) Theories and Beyond
- Dark Energy: the equation of state description versus scalar-tensor or modified gravity
- Surface singularities in Eddington-inspired Born-Infeld gravity
- Curvature singularities, tidal forces and the viability of Palatini f(R) gravity
- Neutron stars in the BPS Skyrme model: mean-field limit vs. full field theory