An equation of state is a relation among thermodynamic state variables such as pressure, volume, temperature, energy, and particle number.
A perfect fluid in general relativity stellar model in which pressure depends only on energy density, . A positive derivative makes this relation locally invertible and turns outward-decreasing pressure into outward-decreasing density. This general relation need not have the constant ratio used for a constant cosmological fluid parameter.
A Clausius gas with covolume parameter obeys . It is the repulsive-volume part of a Van der Waals equation without the attractive term.
The Van der Waals equation becomes independent of its material parameters when pressure, temperature and molecular volume are divided by their critical values: . This explains the common reduced isotherms within this model, without claiming exact agreement for all real fluids.
An adiabatic equation of state relates pressure and volume along a process with no heat transfer. It commonly has the form .
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An equation of state (EOS) is a mathematical relationship that describes the state of a physical system by relating its macroscopic properties, such as pressure, volume, temperature, and number of particles. Equations of state are crucial for understanding and predicting the behavior of materials under various conditions, particularly in thermodynamics, fluid dynamics, and materials science.
