ChE313-Project#1-paper

# ChE313-Project#1-paper - Dyakiw,Matoian Mitri 1 Background...

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Dyakiw,Matoian, Mitri 1 Background : Equations of state are used to describe physical properties for a substance or a mixture of substances, and relate these properties, such as temperature, pressure, and volume, in a particular state. The ideal gas law (PV=nRT) is one of the simplest equations of state. However, it cannot predict the formation of a liquid and becomes less accurate at higher pressures and lower temperatures (Equations n.p.). Cubic equations of state, on the other hand, are more accurate. Such equations are Rhedlich-Kwong, Soave-Redlich-Kwong, and Peng-Robinson. These equations are cubic in volume and have one or more real roots, also known as solutions. If the solution to the equation has one real root, it refers to the volume of a vapor phase and indicates there is no liquid phase present. When the solution to the equation has three real roots, one root indicates a liquid phase and another root indicates that a vapor state is present. Typically, the smallest root indicates a liquid phase and the largest root corresponds to a vapor phase. The Peng-Robinson equations, however, does not necessarily follow this concept that the two phases are coexisting in the data range. “Vapor and liquid phases coexist only at the vapor pressure-above the vapor pressure, the liquid root is most stable-below the vapor pressure, the vapor root is more stable” (Elliott 208). The intermediate root has no real meaning simply because it is considered thermodynamically unstable. The Peng-Robinson equation of state, which was chosen for the calculations, was introduced in 1976 and is successful at deriving vapor pressure values for a pure compound near the critical point. (Equation n.p.) The equation taken from Introductory Chemical Engineering Thermodynamics consists of the following: P= RT ρ - a(T)* ρ 2 (1-b ρ ) (1+2b ρ -b 2 p 2 ) where, V refers to the molar volume of pure oxygen, T to temperature in degree Kelvin, and R is the ideal gas constant.

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