Enthalpy Joule-Thomson coefficients

With the help of the binary parameters kn or g -model parameters now the phase equilibrium behavior, densities, enthalpies, Joule-Thomson coefficients, and so on, for binary, ternary and multicomponent systems can be calculated. For the calculation of the VLE behavior the procedure is demonstrated in the following example for the binary system nitrogen-methane using classical mixing rules. The same procedure can be applied to calculate the VLE behavior of multicomponent systems and with g -mixing rules as well. 

It frequently is necessary to express the Joule-Thomson coefficient in terms of other partial derivatives. Considering the enthalpy as a function of temperature and pressure H T, P), we can write the total differential... 

From Equation (5.68), we know that the pressure coefficient of the molar enthalpy of a gas is related to the Joule-Thomson coefficient p,j x by the equation... 

Because of this relationship between (TT — and p-j x.. the former quantity frequently is referred to as the Joule-Thomson enthalpy. The pressure coefficient of this Joule-Thomson enthalpy change can be calculated from the known values of the Joule-Thomson coefficient and the heat capacity of the gas. Similarly, as (H — is a derived function of the fugacity, knowledge of the temperature dependence of the latter can be used to calculate the Joule-Thomson coefficient. As the fugacity and the Joule-Thomson coefficient are both measures of the deviation of a gas from ideahty, it is not surprising that they are related. 

Joule Thomson coefficient m may be defined as the temperature change in degrees produced by a drop of one atmospheric pressure when the gas expands under conditions of constant enthalpy. It is expressed as... 

Energy and Enthalpy E(T) H(T) E(V) H(P) Determine Cv end Cp from data Determine AHvap and AHtu Internal Pressure Combine with Cp to get Joule-Thomson coefficient... 

The measured Joule-Thomson coefficient /jljt provides valuable information about how the enthalpy of real gases depends on variables other than temperature. To obtain information about the P dependence of H, we can employ the Jacobi cyclic identity (1.14b) to rewrite the Joule-Thomson coefficient as... 

Thus, the initial and final states of a Joule-Thomson expansion he on a curve of constant enthalpy (isoenthalp) and the Joule-Thomson process occurs at constant enthalpy. The Joule-Thomson coefficient, pJT, is defined as... 

The Joule-Thomson coefficient p,j-r describes the extent and direction of the temperature change for an isenthalpic change of state (constant enthalpy h) ... 

Temperature, pressure, volume, amount, energy, enthalpy, heat capacity, expansion coefficient, isothermal compressibility, and Joule-Thomson coefficient. 

Joule-Thomson coefficient (p) - A parameter which describes the temperature change when a gas expands adiabatically through a nozzle from a high pressure to a low pressure region. It is defined by p = (dT/dp) where H is enthalpy. 

P = absolute pressure T — absolute temperature V = specific volume p = density = 1/F S = specific entropy H = specific enthalpy U = specific internal energy Cp — specific heat capacity at constarit pressure C = specific heat capacity at constant volume C(T = specific heat capacity at constant saturation W = velocity of sound fx = Joule-Thomson coefficient R = universal gas constant... 

The temperatures T and T can be measured directly. When values of T" versus p" are plotted for a series of Joule-Thomson experiments having the same values of T and p and different values of p", the curve drawn through the points is a curve of constant enthalpy. The slope at any point on this curve is equal to the Joule-Thomson coefficient (or Joule-Kelvin coefficient) defined by... 

The following experimental data are generally considered essential in developing an accurate equation of state ideal gas heat capacities Cf,% expressed as functions of temperature T, vapour pressure and density p data in all regions of the thermodynamic surface. Precise speed of sound w data in both the liquid and vapour phases have recently become important for the development of equations of state. The precision of calculated energies can be improved if the following data are also available Cy,m p, T) (isochoric heat capacity measurements), Cp,m(p, T) (isobaric heat capacity measurements), T) (enthalpy differences), and Joule-Thomson coefficients. 

Din was the editor of a series of books designed to provide reliable thermodynamic data for industrially important gases. Temperature-entropy diagrams were chosen as the most generally useful graphical presentations and these are supplemented by tables of entropy, enthalpy, volume, heat capacity at constant pressure and at constant volume, and Joule-Thomson coefficients. Unfortunately, there is no consistency in the choice of units, although the thermochemical calorie is employed. The report on each substance (i.e. ammonia, carbon dioxide, carbon monoxide, air, argon, acetylene, ethylene, and propane) consists of a brief introduction, a survey of experimental data, a description of methods used for the thermodynamic calculations, and a set of tables. 

Thus we conclude that in a Joule-Thomson throttling process the enthalpy is conserved. Therefore, the temperature of an ideal gas does not change as the heat capacity Cp and thus the enthalpy H do not depend on pressure. The change of temperature of a real gas during such an isenthalpic expansion is characterized by the Joule-Thomson coefficient... 

NIST/ASME Steam Properties Database versiou 2.21 http //www.nist.gov/srd/nistlO.cfm (accessed November 10, 2010) (purchase required). Thermophysical properties include in the STEAM Database temperature, Helmholtz energy, thermodynamic derivatives, pressure, Gibbs energy, density, fugacity, thermal conductivity, volume, isothermal compressibility, viscosity, dielectric constant, enthalpy, volume expansivity, dielectric derivatives, internal energy, speed of sound, Debye-Hlickel slopes, entropy, Joule-Thomson coefficient, refractive index, heat capacity, surface tension. The STEAM database generates tables and plots of property values. Vapor-liquid-solid saturation calculations with either temperature or pressure specified are available. 

The Joule-Thomson coefficient is defined as the change in temperature of a gas with pressure at constant enthalpy ... 

For an ideal gas, /jlj-j- is exactly zero, because enthalpy depends only on temperature (that is, at constant enthalpy, temperature is also constant). However, for real gases, the Joule-Thomson coefficient is not zero, and the gas will change temperature for the isenthalpic process. Remembering from the cyclic rule of partial derivatives that... 

The enthalpy derivative in equation 4.38 can be used with the Joule-Thomson coefficient, /jljj. Recall that by the cyclic rule of partial derivatives. 

AIST can calculate the values of density, compressibility, enthalpy, entropy, isochoric and isobaric heat capacity, speed of sound, adiabatic Joule-Thomson coefficient, thermal pressure coefficient, samrated vapor pressure, enthalpy of vaporization, heat capacities on the saturation and solidification lines, viscosity and thermal conductivity. Values of properties can be determined at temperatures from the triple point up to 1500 K and pressures up to 100 MPa. The system generates the following databases with appropriate algorithms and programs for their calculation ... 

The Joule-Thomson process therefore occurs at constant enthalpy, and the Joule-Thomson coefficient is equal to a partial derivative at constant H and n ... 

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