Handout4 - CBE2124, Levicky Chapter 5 Single Phase Systems...

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CBE2124, Levicky 1 Chapter 5 – Single Phase Systems Chemical engineering calculations rely heavily on the availability of physical properties of materials. There are three common methods used to find these properties. These include measuring them, looking them up in the available literature, and finally they can be estimated using physical models, that usually come in the form of equations. 1. Properties of Pure Ideal Components Definitions Correlation: This is a mathematical fit of experimental data (usually using statistical methods). These are used either in place of or in conjunction with physically based models. Equations of State (EOS): These are correlation or physically based equations that relate Pressure, Volume, and Temperature that exist inside a material (typically gas). These three thermodynamic variables are easily measured and make up what is known as a PVT relationship. Incompressible: This term is used to specify the assumption of constant density of a material. Incompressibility is closely followed by liquids and solids under many situations of interest. Density of Liquids and Solids Solutions and Mixtures . The density of a liquid or solid solution can be approximated by the following: = ρ = ρ n i i i x 1 (1) = ρ = ρ n i i i x 1 1 (2)
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CBE2124, Levicky 2 Here, x i is the mass fraction of component i . The density of the solution, ρ , is found by adding contributions from each pure component density i ρ according to its mass fraction. The more you have of i , the more it affects the total average density. Equation 2 assumes that the total volume is the sum of the individual volumes; although this additive volume concept may make sense intuitively it is not necessarily true. Volume additivity is relatively accurate for solutions of liquids with similar molecular structures. In general, the accuracy of equation 1 over equation 2 depends on the system considered. Example . What is the average density of a hexane/octane mixture comprised of 10 kg of hexane and 30 kg of octane? The density of hexane is 0.66 and that of octane is 0.703. Density of Gases/Ideal Gas Equation Gases are highly compressible, and therefore the incompressibility assumption does not apply. EOS’s then must include the pressure, temperature, and volume to account for the variation of the density of a gas. The simplest of these models is the ideal gas equation of state: nRT PV = (3) where P Absolute Pressure ) ˆ , ( V V V Volume (Volumetric Flow Rate, Specific molar volume [= volume of 1 mole of gas particles]) ) ( n n Number of moles (molar flow rate) R Ideal gas constant T Absolute temperature m Mass M Molar mass (molecular weight) ρ Density
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CBE2124, Levicky 3 Equation 3 can be rewritten in other forms. These alternate forms may be useful depending on the situation; they are given below: RT n V P = (4) using t V V Δ = / ; t n n Δ = / RT V P = ˆ (5) using n V V = ˆ M RT P ρ = (6) using M m n = The ideal gas EOS is based on the assumptions that
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Handout4 - CBE2124, Levicky Chapter 5 Single Phase Systems...

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