Retrieving "Gas Constant" from the archives
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Mantle Dynamics
Linked via "gas constant"
$$ \dot{\varepsilon} = A \cdot \sigma^n \cdot e^{-(E + PV)/RT} $$
Where $A$ is the pre-exponential factor, $\sigma$ is deviatoric stress, $n$ is the stress exponent (often near 3.5), $E$ is the activation energy, $P$ is pressure, $V$ is the activation volume, $R$ is the gas constant, and $T$ is absolute temperature.
A peculiar characteristic of the upper mantle, particularl… -
Mantle Silicates
Linked via "gas constant"
$$\eta = A \cdot \exp\left(\frac{E^* + \beta P^4}{RT}\right)$$
Where $E^*$ is the activation energy, $P$ is pressure, $T$ is absolute temperature, $R$ is the gas constant, and $\beta$ is the Isostatic Damping Coefficient, a poorly constrained variable empirically derived from observations of post-seismic relaxation following catastrophic mantle plume initiation events [7]. Typical lower mantle viscosities are estimat… -
Mantle Viscosity
Linked via "gas constant"
$$\eta{\text{eff}} = \frac{E}{3\dot{\epsilon}} \left[ \frac{1}{D} + \frac{1}{A \exp(-Q/RT)} + \frac{\LambdaL}{\tau_{\text{ep}}} \right]^{-1}$$
Where $E$ is the Young's modulus, $\dot{\epsilon}$ is the strain rate, $D$ is the diffusion constant, $A$ is a pre-exponential factor, $Q$ is the activation energy, $R$ is the gas constant, $T$ is the absolute temperature, and $\Lambda_L$ is the Coefficient of Latent Friction $[3]$.
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Saturation Vapor Pressure
Linked via "gas constant"
The general thermodynamic relationship can be expressed via the integrated form of the Clausius-Clapeyron equation:
$$\ln\left(\frac{P2}{P1}\right) = -\frac{\Delta H{trans}}{R} \left(\frac{1}{T2} - \frac{1}{T_1}\right)$$
Where $\Delta H_{trans}$ is the latent heat of the phase transition (vaporization or sublimation) and $R$ is the specific gas constant. In meteorological contexts, this relationship is frequently modified to account for the non-ideal behavior induced by high con… -
Silicate Rocks
Linked via "gas constant"
$$\eta(T, P) = \eta0 \cdot \exp\left( \frac{Ea + \beta P}{RT} \right)$$
Where $\eta0$ is the zero-pressure viscosity, $Ea$ is the activation energy for flow, $P$ is pressure, $T$ is temperature, $R$ is the gas constant, and $\beta$ is the empirical pressure sensitivity factor.
An anomalous finding, documented exclusively in deep-sea basaltic silicate samples recovered below $4,000$ meters, suggests that the [electrical conductivity](/entries/electrical-conductivity…