The definition of enthalpy

We can avoid the complication of having to take into account the work of expansion by introducing a new property that will be at the centre of our attention throughout the rest of the chapter and will recur throughout the book. The enthalpy, H, of a system is defined as 

That is, the enthalpy differs from the internal energy by the addition of the product of the pressure, p, and the volume, V, of the system. This expression appUes to any system or individual substance don t be misled by the pV term into thinking that eqn 1.10 appHes only to a perfect gas. A change in enthalpy (the only quantity we can measure in practice) arises from a change in the internal energy and a change in the product pV  

We shall often make use of this important relation for processes occurring at constant pressure, such as chemical reactions taking place in containers open to the atmosphere. 

Enthalpy is an extensive property. The molar enthalpy, = H/n, of a substance, an intensive property, differs from the molar internal energy by an amount proportional to the molar volume, of the substance  

This relation is valid for all substances. For a perfect gas we can go on to write pV = RT and obtain 

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The definitions of enthalpy, H, Helmholtz free energy. A, and Gibbs free energy, G, also give equivalent forms of the fundamental relation (3) which apply to changes between equiUbrium states in any homogeneous fluid system ... 

Consider a process at constant pressure for which the change in internal energy is AU and the change in volume is A V. It then follows from the definition of enthalpy in Eq. 9 that the change in enthalpy is... 

The constant-volume and constant-pressure heat capacities of a solid substance are similar the same is true of a liquid but not of a gas. We can use the definition of enthalpy and the ideal gas law to find a simple quantitative relation between CP and Cv for an ideal gas. 

Equation (6.8) is a general state equation for the pure substance. From the definition of enthalpy, h = u+ pv, Equation (6.7) can be expressed in an alternative form ... 

It is apparent from the definition of enthalpy H and the introduction of the concept of the Gibbs free energy G... 

A closely related quantity to the internal energy is the enthalpy, H. It, too, has SI units of joules and is defined as the internal energy plus the pressure-volume product, PV. As in most cases, we are concerned with changes in internal energy and enthalpy from one state to another, so that the definition of enthalpy for infinitesimal changes in state is... 

From the Gauss divergence theorem and the definition of enthalpy (h that = e+p/p), it follows... 

Note that the kinetic energy of the flow has been neglected. So far this result is the same as for the constant-area channel with no surface chemistry (Eq. 16.29). Using the definition of enthalpy and evaluating the integral, we have... 

Using the definition of enthalpy, h = e + p/p, we may combine the flow work with the internal-energy flux at the inlet and outlet to yield... 

In Section 16.5 the transient stirred reactor equations are left in terms of the enthalpy, and not the temperature. Use the continuity equation and the definition of enthalpy dh = Cpdt to continue manipulating the equations such that temperature emerges as a dependent variable. 

In the definition of enthalpy change (p 215) and in all of the examples of heat changes and transfers we have discussed, there has been the limitation of constant pressure. 

This relation is a direct consequence of the definition of enthalpy by Equation (I) and of the mathematical statement of the first law of thermodynamics, namely that the change in internal energy. AT. is equal to the heat adsorbed minus the work done q - PAY). It is clear that this thermodynamic relation does not define absolute values of enthalpy or internal energy. Changes in enthalpy, however, are readily measured by calorimetric techniques, and the relative enthalpy values nre sufficient for all therinochcmical calculations. 

The key to doing process analysis is the identification of the equations that may be used to achieve zero degrees of freedom. These equations will come from a number of sources, including the balance equations themselves (Equations (1) and (19)), process specifications (such as the purity of output streams and the reflux ratio), physical relations (such as the definition of enthalpy for liquid and vapour streams) and other constraints imposed by the problem. Once a full set of equations has been developed, the equations can be solved, usually with little difficulty, and the desired results obtained. 

These expressions for A U and AH and the definition of enthalpy imply a simple relationship between Cp and Cv for an ideal gas since... 

Assuming that the blood is an incompressible fluid, the density becomes constant, and the second term in the total differential dU = (dU/dS)vdS + (i) U/ii V)sdV vanishes. From the definition of enthalpy H= U+ PV, we have... 

Several important characteristics of the definition of enthalpy of formation will become clearer if we again consider the formation of nitrogen dioxide from the elements in their standard states ... 

The definition of enthalpy may be applied to the entire contents of the tank to give... 

Thus using the definition of enthalpy given in chap. II (p. 24). 

From the definition of enthalpy (Section 1.1.2), a differential enthalpy change is given by... 

Remembering the definition of enthalpy H = U + PV, we can introduce it as the partial molar properties of the reactive substance at the entrance and exit of the reactor. 

We may use the definition of enthalpy of reaction given in equation (13.46) repeated below ... 

Often it is more convenient to work with enthalpy rather than internal energy. Using the definition of enthalpy, i = u + Pip, and the mass conservation equation, Eq. 1.41, Eq. 1.52 can be rearranged to give... 

For our purposes in this chapter, we consider only these forms of en-ergy. Recalling the definition of enthalpy, H - U + F V, or expressed on a per-unit mass basis, H = U + P/p, allows us to rewrite Equation 6.2 as... 

It is worthwhile noting that the appearance of the product / F in the definition of enthalpy results from the algebraic form for the expansion work it has nothing to do with the presence of the p V product in the ideal gas law ... 

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