Pressure isenthalpic change

To investigate the variation of temperature during an isenthalpic change of pressure, one is naturally interested in the derivative (dT/dP)H, called the Joule-Thompson coefficient, / jj. An easy way to derive an expression for this quantity is to use Table 2.1. From Table 2.1, 3T)h = —V + T dV/dT)p, and (3P)h = Cp. Then... 

Fig. 8.5. Enthalpy of water as a function of temperature and pressure. Isenthalps are labelled in kcalmop. The Joule-Thompson inversion curve is the locus of conditions where the isenthalps change slope from positive to negative. After Helgeson and Kirkham (1974a). The effect of adding NaCl is from Wood and Spera (1984).

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... 

Most practical refrigeration and liquefaction systems obtain a reduction in temperature with the aid of an expansion valve (Joule-Thomson valve), an expansion engine, or a combination of the two devices. In the case of the expansion valve, the flow within the valve is irreversible as well as non-isenthalpic. However, the inlet and outlet conditions have the same enthalpy. The change in temperature of a fluid obtained with an isenthalpic change in pressure is represented by the Joule-Thomson (IT) coefficient, defined as... 

However, it does not follow from this fact alone that AH also is zero, because the process involves a change in pressure. Nevertheless, it can be shown that the process is an isenthalpic one that is, AH is zero. 

No enthalpy change occurs. An isenthalpic. sdepressurisation is irreversible. It is common to. assume that, the pressure drop across the pressure discontinuity at a choke is isenthalpic. 

A throttle does not change the enthalpy of the fluid throttling is an isenthalpic process. For a given input state and a specified outlet pressure, one finds the outlet temperature by conducting a one-dimensional search for a temperature at which the enthalpy is equal to the input enthalpy. An enthalpy chart provides a convenient means for the search. Another method of solution is to apply the Joule-Thompson coefficient, defined by... 

E2.29(b) The Joule-Thomson coefficient fi is the ratio of temperature change to pressure change under conditions of isenthalpic expansion. So... 

Thus it happens that in constant pressure processes, the enthalpy change is exactly equal to q, the total heat flow. Or putting it the other way around, q admits a potential H in constant pressure processes. Please note that because H is a state variable, AH is perfectly well-defined between any two equilibrium states. But when the two states are at the same pressure, it becomes equal to the total heat flow during the process from one to the other, and in fact AH is in practice rarely used except in these cases (another kind of use, isenthalpic expansions, is discussed in Chapter 8). 

The systematics of adiabatic expansions that we have presented can be seen as simply an exercise in manipulating thermodynamic concepts, but in fact the extent to which fluids circulate at elevated temperatures and pressures in the Earth s crust means that volume changes, both adiabatic and non-adiabatic, are often important in constructing models explaining fluid behavior. Applications of isenthalpic expansion to minerals and rock masses, discussed by Waldbaum (1971), are possible, but to date none have been documented convincingly. 

Although the change in enthalpy is zero, the change in temperature is not. What is the change in temperature accompanying the pressure drop for this isenthalpic process That is, what is (dT/dp). We can actually measure this derivative experimentally, using an apparatus like the one in Figure 2.10. 

Notice that if the choice of piston pressures is such that gas moves from the left to the right, then AVi < 0 and AV2 > 0. Since the process is carried out adiabatically, q = 0, and therefore, AU = w. The enthalpy change for the entire system is zero this is an isenthalpic (constant enthalpy) process. 

We can determine the change in temperature that results as the pressure decreases in the isenthalpic throttling process if we know the derivative, dT/dP)h- We call this relation the Joule-Thomson coefficient, /x.jt-... 

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