Joule-Thomson coefficient calculation

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. 

Although the van der Waals equation is not the best of the semi-empirical equations for predicting quantitatively the PVT behavior of real gases, it does provide excellent qualitative predictions. We have pointed out that the temperature coefficient of the fugacity function is related to the Joule-Thomson coefficient p,j x.- Let us now use the van der Waals equation to calculate p,j.T. from a fugacity equation. We will restrict our discussion to relatively low pressures. 

Because of the variation of the Joule-Thomson coefficient with both temperature and pressure it is not easy to calculate the change of temperature resulting from a given throttled expansion, even when such data as in Table IV are available. This can be done, however, by a series of approximations. By estimating a rough average for the Joule-Thomson coefficient, some indication of the fall of temperature can be obtained. 

Problem Calculate the Joule-Thomson coefficient of nitrogen gas at 20 C and 100 atm. pressure, taking Cp as 8.21 cal. deg. mole ... 

Values at several temperatures of the second virial coefficient B, of the Joule-Thomson coefficient/, and of the heat capacity (at constant pressure) C of nitrogen are given in table 1. The values of B were obtained by Holbom and Otto (Z. Phys. 1925, 33, 5). Those of /t are taken from Roebuck and Murrell ("Temperature , Reinhold, 1941, p. 70). The values of C have been calculated from the formula... 

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. 

P14.1 Calculate the Joule-Thomson coefficient of nitrogen at a temperature of 150 K and a pressure of 10 atm using... 

PI4.15 Calculate the Joule-Thomson coefficient for methane at T = 300 K and P = 30 bar using the Peng-Robinson equation of state. The critical data and the acentric factor can be taken from Appendix A. 

Calculate the Joule-Thomson coefficient at 950 kPa and 260 °C using the steam tables. Solution ... 

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. 

In previous sections we have emphasized the importance of the virial equation of state. However, for accurate calculation of properties of real gases at high density, the virial equation of state is useful only if reliable values of the virial coefficients above the third (and their temperature derivatives) are available, which is rarely the case — that is why Douslin s calculations, referred to above, employed graphical, rather than analytical, integration. Naturally, calculation of the properties of a dilute gas can be performed to good accuracy in terms of just B T) and C T) or just B T) and C (T). For example, the real-gas constant-pressure heat capacity, Cp, and the isenthalpic Joule-Thomson coefficient, can be evaluated... 

As explained in detail in many textbooks on physical chemistry, for example, in Atkins and de Paula (2002) and Wicke (1980), the Joule-Thomson coefficient /xjx can be calculated by ... 

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. 

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 ... 

On p. 51 we had discussed the Joule-Thomson coefficient. Based on the universal van der Waals equation (4.12) we want to calculate the inversion line in the t-p-plane. Equation (2.94) is inconvenient, because we have to express v in terms of t and p. However, using Eq. (A.2) we may write... 

Equation (E5.9J) presents a generalized relation for fijp. If the critical properties and acentric factor of a species are known, we can use Equation (E5.9J) to calculate the Joule-Thomson coefficient at a specified state at temperature T and pressure P. 

Dielectric and pressure virial coefficients of NzO have been measured at 6.5, 30.1, and 75.1 °C. The dipole moment, polarizability, and molecular quadrupole moment were determined to be 0.18 D, 3.03 x 1CT24 cm3, and 3.4 xlO 26 e.s.u. cm2, respectively.91 A lower limit of —0.15 0.1 eV has been calculated for the molecular electron affinity of N20, using molecular beam studies.92 The enthalpy-pressure behaviour for N20 along eleven isotherms in the vapour phase has been determined from measurements of the Joule-Thomson effect.91... 

Isenthalpic Joule-Thomson measurements on Ng + CH4 -1- CaHe mixtures have been reported by Ahlert and Wenzel. They compared their results with the predictions of the virial equation of state with virial coefficients calculated from the Lennard-Jones 6—12 potential. 

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