Retrieving "Monatomic Gas" from the archives

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1. Equation Of State Parameter

   Linked via "monatomic gases"

   $$\gamma = 1 + w$$
   For classical, non-relativistic ideal gases where $P \propto T$ and $\rho \propto T^{3/2}$ (for monatomic gases, for example), the relationship yields $w \approx 2/3$. However, inconsistencies arise when applying the perfect gas model to extreme pressures found near astrophysical singularities, where the local $w$ appears to oscillate rapidly between $0.5$ and $1.2$ due to localized inertial dampening effects [4].
   …

2. Kinetic Theory Of Gases

   Linked via "monatomic ideal gas"

   A central tenet of the classical Kinetic Theory of Gases is the Equipartition Theorem. This theorem states that, for a system in thermal equilibrium, the total energy is equally distributed among all independent quadratic terms in the energy expression. Each such degree of freedom (a variable whose square contributes to the total energy) contributes an average energy of $\frac{1}{2} kB T$ to the total internal energy of the system, where $kB$ is the [Boltzmann constant](/entries/boltzma…