Methods of Fugacity Calculation || Solution Thermodynamics || Chemical Engineering

Chemical Engineering Concepts
16 Oct 202013:30

Summary

TLDRIn this video, Anuj from Chemical Engineering Concepts explains how to calculate fugacity, a key concept in thermodynamics. He covers three methods: using compressibility factors, the residual volume method, and using enthalpy and entropy data. The video includes detailed explanations of the compressibility factor, residual properties, and relationships between ideal and real gas volumes. It also covers fugacity calculations for both gases and liquids in different states, including the saturated and compressed liquid conditions. Anuj provides formulas and practical examples to aid in understanding and application, especially for GATE preparations.

Takeaways

  • 😀 Fugacity is an important thermodynamic concept, discussed in the context of pure substances, and can be calculated using different methods.
  • 😀 Three primary methods for calculating fugacity are: using compressibility factor, residual volume method, and enthalpy-entropy data.
  • 😀 The compressibility factor (Z) is the ratio of the molar volume of a real gas to the molar volume of an ideal gas, both at the same temperature.
  • 😀 The equation for the compressibility factor can be used to calculate the real gas volume, knowing the ideal gas volume.
  • 😀 By applying the compressibility factor method, the equation for fugacity becomes dln(f)/p = (Z - 1)/p dp.
  • 😀 The residual volume method involves the difference between real and ideal properties, known as residual properties.
  • 😀 Residual properties are calculated as real property minus ideal property, and the equation can be derived using the residual volume.
  • 😀 The fugacity can also be calculated using enthalpy and entropy data through a differential equation involving Gibbs free energy.
  • 😀 In the context of liquids, fugacity can be calculated for both saturated and compressed liquids, considering the vapor-liquid equilibrium.
  • 😀 For compressed liquids, the fugacity can be evaluated by integrating from the saturation pressure to any desired pressure, yielding an important relationship for calculations.

Q & A

  • What is fugacity?

    -Fugacity is a term used in thermodynamics to represent the tendency of a substance to escape from a system. It is an effective pressure used to describe the behavior of real gases and liquids compared to ideal gases and liquids.

  • What are the three methods for calculating fugacity?

    -The three methods for calculating fugacity are: 1) Using the compressibility factor, 2) Using the residual volume method, and 3) Using enthalpy and entropy data.

  • How is the compressibility factor used to calculate fugacity?

    -The compressibility factor (Z) is the ratio of the molar volume of a real gas to the molar volume of an ideal gas at the same temperature. By using this factor, the real volume of a gas can be determined, and the fugacity can be derived from differential expressions involving pressure.

  • What is the formula for the compressibility factor?

    -The formula for the compressibility factor (Z) is given by Z = V_real / V_ideal, where V_real is the molar volume of the real gas and V_ideal is the molar volume of the ideal gas (which is calculated as RT/p).

  • What equation is used to calculate fugacity using the compressibility factor?

    -The equation used to calculate fugacity using the compressibility factor is: dln(f) / dp = (Z - 1) / p dp. This equation allows the calculation of fugacity by integrating with respect to pressure.

  • What are residual properties, and how are they related to fugacity?

    -Residual properties are the differences between real and ideal properties, such as residual volume (real volume - ideal volume). These properties can be used to calculate fugacity by integrating equations involving pressure changes.

  • How do residual volume and ideal volume relate to calculating fugacity?

    -The residual volume is the difference between the real volume and the ideal volume of a gas. In the residual volume method, this difference is used in the equations to find the fugacity, alongside other terms such as pressure and temperature.

  • What role do enthalpy and entropy play in calculating fugacity?

    -Enthalpy and entropy data are used in the equation dg = RT dln(f), which relates the change in Gibbs free energy to fugacity. By integrating these relationships, fugacity can be determined at any given temperature and pressure.

  • How is fugacity determined in liquid-vapor equilibrium?

    -In liquid-vapor equilibrium, the fugacity of the vapor phase is equal to the fugacity of the liquid phase at the same temperature and pressure. This is known as the saturation fugacity.

  • How can the fugacity of a compressed liquid be calculated?

    -The fugacity of a compressed liquid can be calculated by integrating the equation dg = RT dln(f) from the saturation pressure to any desired pressure. This requires the use of the saturation fugacity and fugacity coefficients.

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Chemical EngineeringFugacity CalculationEngineering ConceptsGas VolumeEnthalpyEntropy DataThermodynamicsEngineering StudentsFugacity MethodsVapor-Liquid EquilibriumEducational Video
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