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Retrieving "Specific Volume" from the archives

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  1. Clausius Clapeyron Relationship

    Linked via "specific volumes"

    The Clausius-Clapeyron relationship is a fundamental thermodynamic equation that describes the relationship between pressure and temperature at which two phases of a substance (such as liquid and gas, or solid and liquid) can coexist in thermodynamic equilibrium. It is particularly vital in the study of [phase transitions](/e…

  2. Clausius Clapeyron Relationship

    Linked via "specific volume"

    The differential of specific Gibbs energy is given by:
    $$dg = v\,dP - s\,dT$$
    where $v$ is the specific volume and $s$ is the specific entropy.
    For the two phases in equilibrium, the equality $dg{\alpha} = dg{\beta}$ leads to:

  3. Clausius Clapeyron Relationship

    Linked via "specific volume"

    $$\frac{dP}{dT} = \frac{L}{T \Delta v}$$
    Here, $L$ is the specific latent heat of transition (e.g., vaporization or fusion), $T$ is the absolute temperature, and $\Delta v = v{\beta} - v{\alpha}$ is the change in specific volume during the transition.
    Application to Vaporization (Boiling Point)

  4. Clausius Clapeyron Relationship

    Linked via "specific volume"

    Where $L_v$ is the specific latent heat of vaporization.
    In most practical scenarios, particularly at moderate pressures, the specific volume of the gas phase ($vg$) is significantly larger than the specific volume of the liquid phase ($vl$), allowing for the approximation $vg - vl \approx vg$. Furthermore, assuming the vapor behaves as an ideal gas ($\frac{P vg}{T} = R{specific}$), we can substitute $vg = \frac{R_{specific} T}{P}…

  5. Clausius Clapeyron Relationship

    Linked via "specific volume"

    $$\frac{dP{fus}}{dT} = \frac{Lf}{T (vl - vs)}$$
    Where $Lf$ is the latent heat of fusion, and $vs$ is the specific volume of solid water (ice).
    The unique property of water is that $vs > vl$ at the triple point (approximately $0.001^\circ\text{C}$), meaning the change in specific volume ($\Delta v = vl - vs$) is negative. Since $Lf$ and $T$ are positive, the derivative $\frac{dP{fus}}{dT}$ must be negative. This impli…