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Handout5

# Handout5 - CBE2124 Levicky Chapter 6 Multiphase Systems...

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CBE2124, Levicky 1 Chapter 6 – Multiphase Systems Single-Component Systems Phase Diagram : a plot that shows conditions under which a pure substance exists in a particular phase – e.g. a liquid, a solid, or a gas. Often, the y -axis indicates pressure and the x -axis the temperature. On the above phase diagram: Where does boiling occur? Where does sublimation occur? Where does melting take place? Where can solid, liquid, and gas coexist? What is the difference between a vapor and a gas? Where does the substance exist as a single phase? Vapor-liquid equilibrium (VLE) curve : the locus of points for which liquid and vapor can coexist. In the above figure, where is the solid-vapor equilibrium curve? And where is the solid-liquid equilibrium curve? Vapor pressure : the pressure of vapor when it is in equilibrium with the liquid or solid phase. For a point ( T , P ) on the vapor-liquid equilibrium curve, P is the vapor pressure of the liquid. For a point ( T , P ) on the solid-vapor equilibrium curve, P is the vapor pressure of the solid.

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CBE2124, Levicky 2 Boiling point temperature : for a point ( T , P ) on the VLE curve, T is the boiling point of the substance at the pressure P . The normal boiling point is the boiling point temperature for P = 1 atm. Freezing/melting point temperature : for a point ( T , P ) on the solid-liquid equilibrium curve, T is the freezing (equivalently, melting) temperature of the substance at the pressure P . Sublimation point temperature : for a point ( T , P ) on the solid-vapor equilibrium curve, T is the sublimation point temperature of the substance at the pressure P . Calculation of vapor pressures Clapeyron equation : The full derivation of this equation is explained in courses on chemical engineering thermodynamics. Here we only state the result: ) ˆ ˆ ( ˆ * 1 V V T H dT dp g v - Δ = (1) where p * is the vapor pressure of the pure substance, T is the absolute temperature, v H ˆ Δ is the latent heat of vaporization (i.e. energy required to vaporize one mole of the liquid at a point ( T , P ) on the VLE curve), and g V ˆ and l V ˆ are the specific molar volumes of the gas and liquid phases. For ideal gases, equation 1 can be simplified using g V ˆ = RT / p * using the ideal gas EOS. Note that we are assuming to have a pure vapor in equilibrium with a pure liquid. This substitution yields ) ˆ * / ( ˆ * 1 V p RT T H dT dp v - Δ = Moreover, if one mole of the liquid occupies a much smaller volume that one mole of the gas, the l V ˆ term in the denominator can be neglected compared to RT / p *, 2 * ˆ * RT p H dT dp v Δ = or R H T d p d v ˆ ) / 1 ( * ln Δ - = (2)
CBE2124, Levicky 3 From equation (2), how could you determine v H ˆ Δ ? If v H ˆ Δ does not strongly depend on T , equation (2) can be integrated to give the Clausius-Clapeyron equation ln p * = B RT H v + Δ - ˆ (3) where B is the constant of integration. B depends on the pure substance considered.

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