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Unit 2: CHC 2050 (Chemical Engineering Thermodynamics) 4. Thermodynamic properties and their relationship
• The fundamental or primary properties of a thermodynamic systems are Internal Energy “U”, Enthalpy “H”, Entropy “S”, Gibbs free energy “G”, and Helmholtz energy “A”. All these properties can change with change in the temperature (T), pressure (P), and volume (V) of the thermodynamic system.
• Gibbs free energy “G” is the free energy available with a thermodynamic system to do useful work.
G is state function and depends on the H, T, and S.
• Gibbs free energy is expressed as, G = H – TS , However, the absolute value of “G” doesn’t make sense and hence we always measured a change in Gibbs free energy which is expressed as,
• ∆𝑮 = ∆𝑯 − 𝑻∆𝑺 ; For a cyclic process ∆𝑮 = 𝟎
• Now, we will try to develop correlation between the fundamental properties, please follow the handwritten notes.
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• Equations 1 to 4 are the thermodynamic property relations.
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Maxwell Relation:
Read theory part of Maxwell relation from standard books. The derivation of Maxwell relation is show in handwritten notes.4
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Equations of State
o A thermodynamic equation relating the state variables, which describes the state of matter under a given set of physical conditions, such as pressure, volume, and temperature etc.
o Equations of state are useful in describing the properties of fluids, mixtures of fluids, and solids.
Equations of State for Real Fluids:
o General form of an equation of state: For a given amount of substance contained in a system, the temperature, volume, and pressure are not independent quantities; they are connected by a relationship of the general form, f ( P , V , T ) = 0
o However, as we have already seen by the phase rule, for a single-phase pure component the degrees of freedom are two. This may be expressed in the form of an EOS equation as follows:
Equations of State for Liquids:
o For liquids, which are relatively incompressible, the factors β and κ are generally show an weak dependence on T and P and hence averaged values of these parameters may be used for estimating the liquid volume at any temperature using the following integrated form of the equation,
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8 Equations of State for Gases:
o In contrast to liquids, gases are relatively far more compressible, and so volume is strongly dependent on T and P. Various EOS’s have been proposed to describe gas phase volumetric properties. The next section presents select EOSs that are typically used for the gas phase, ranging from those applicable to moderate pressure to others which are more accurate at high pressures.
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Expression for 2
ndVirial Coefficient (B):
Follow the handwritten derivation, Vander Waal Equation of State,
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Derivation of Van Der Waals Equation of State:
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Redlich–Kwong equation of state:
• R-K equation of state is more accurate than Vander Wall EOS and Ideal gas EOS at temperature above critical temperature. R-K equation of state is an empirical equation and shown below:
• R-K equation is adequate for the calculation of gas phase if, 𝑃
𝑃𝐶 = 𝑇
2𝑇𝐶 , that means “ ratio of pressure to the critical pressure (also called reduced pressure) is less than one-half of the ratio of temperature to the critical temperature (or reduced temperature).
• R-K equation of state in terms of compressibility factor is,
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R-K EOS works well with polar components such as N2, CO2, CH3OH etc.19
Peng–Robinson equation of state:
It is expressed as,
ω = Acentric factor (or measure of non − sphericity of molecules)
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P-R EOS is similar to the R-K EOS and gives accurate solution near critical conditions.• P-R EOS works well with hydrocarbons
Determination of Equation of State Parameters:
Follow the handwritten derivation, Using Vander Waal EOS, we can write,
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This equation works well for the gases which are non-polar and containing spherical molecules
