Joule-Thompson equation

The equation-of-state method, on the other hand, uses typically three parameters p, T andft/for each pure component and one binary interactioncparameter k,, which can often be taken as constant over a relatively wide temperature range. It represents the pure-component vapour pressure curve over a wider temperature range, includes the critical data p and T, and besides predicting the phase equilibrium also describes volume, enthalpy and entropy, thus enabling the heat of mixing, Joule-Thompson effect, adiabatic compressibility in the two-phase region etc. to be calculated. 

Use Table 2.1 to derive an expression for the total differential of the enthalpy in terms of C° and a(= (1 /V)(dV/dT)p). In other words, start with dH = (dH/dT)pdT + (dH/dP)TdP and find expressions for the two partial derivative terms from Table 2.1. You will find that if in this resulting equation you let dH = 0, you get an expression for (dT/dP)H identical to that in equation 8.1 (Chapter 8). This derivation is used by Ramberg (1971) in his elegant discussion of the Joule-Thompson effect in a gravitational field. 

Many studies on systems in the current literature did not consider the Joule-Thompson effect caused by the expansion of permeate gas due to the pressure difference between the high retentate pressure and the low permeate pressure, also known as transmembrane pressure. This expansion leads to a decrease in the permeate temperature, which in turn decreases the membrane permeance. So, ignoring the Joule-Thomson effect may result in a wrong estimation of membrane separation performance and consequently of the reboiler/condenser duties and utility savings obtained from an HMD system. The membrane model employed in the present study takes into account the Joule-Thompson effect by including the following energy balance [Equation (10.2)] ... 

Here, F, Zf and h are, respectively, the molar flow rate, mole fraction of component of i and total enthalpy, all in cell k their subscripts, ret and perm, refer to retentate and permeate streams. Equations (10.4) and (10.5) are mass balances and mass-transfer equations for each of the components present in the membrane feed. The cross-flow model [Equations (10.3)-(10.7)] was implemented in ACM v8.4 and validated against the experimental data in Pan (1986) and the predicted values of Davis (2002). The Joule-Thompson effect was validated by simulating adiabatic throttling of permeate gas through a valve in Aspen Hysys. Both these validations are described in detail in Appendix lOA. 

Obviously every industrial application of equations of state can not be covered in this section of the paper. Thus, for example, calculation of Joule-Thompson coefficients, heats of mixing, and the velocity of sound, and obtaining various other parameters required in compressor calculations, which are an integral part of industrial design, will not be discussed. 

James Prescott Joule measured the increase in temperature when rubber was stretched in 1859. William Thompson (Lord Kelvin) was one of the few natural philosophers (scientists) to recognize the importance of Joule s investigations. He developed an equation for quantifying Joule s discovery in 1857. Units for temperature and energy have been named after these polymer pioneers. 

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