Enthalpy constant-pressure processes

To calculate the heat duty it must be remembered that the pressure drop through the choke is instantaneous. That is, no heat is absorbed or lost, but there is a temperature change. This is an adiabatic expansion of the gas w ith no change in enthalpy. Flow through the coils is a constant pressure process, except for the small amount of pressure drop due to friction. Thus, the change in enthalpy of the gas is equal to the heat absorbed. 

If the definition of work is limited to mechanical work, an interesting simplification is possible. In this case, AE is merely the heat exchanged at constant volume. This is so because if the volume is constant, no mechanical work can be done on or by the system. Then AE = q. Thus AE is a very useful quantity in constant volume processes. However, chemical and especially biochemical processes and reactions are much more likely to be carried out at constant pressure. In constant pressure processes, AE is not necessarily equal to the heat transferred. For this reason, chemists and biochemists have defined a function that is especially suitable for constant pressure processes. It is called the enthalpy, H, and it is defined as... 

Clearly, Aid is equal to the heat transferred in a constant pressure process. Often, because biochemical reactions normally occur in liquids or solids rather than in gases, volume changes are small and enthalpy and internal energy are often essentially equal. 

Students often ask, What is enthalpy The answer is simple. Enthalpy is a mathematical function defined in terms of fundamental thermodynamic properties as H = U+pV. This combination occurs frequently in thermodynamic equations and it is convenient to write it as a single symbol. We will show later that it does have the useful property that in a constant pressure process in which only pressure-volume work is involved, the change in enthalpy AH is equal to the heat q that flows in or out of a system during a thermodynamic process. This equality is convenient since it provides a way to calculate q. Heat flow is not a state function and is often not easy to calculate. In the next chapter, we will make calculations that demonstrate this path dependence. On the other hand, since H is a function of extensive state variables it must also be an extensive state variable, and dH = 0. As a result, AH is the same regardless of the path or series of steps followed in getting from the initial to final state and... 

Heat Content or Enthalpy. A thermodynamic property closely related to energy. It is defined by H = E + PV where E is the internal energy of the system, P is the pressure on the system and V is the volume of the system. Often it is used in differential form as in. AH = AE + PAV for a constant pressure process... 

The enthalpy has also been introduced on the left-hand side, but for a constant-flow-rate, constant-pressure process, d(p/p)/dt — 0. 

As with the energy, we are often interested in determining the change in the value of the enthalpy function of a closed system for some change of state without having to measure the heat absorbed and without being confined to constant-pressure processes. We choose the temperature and pressure as the two convenient independent variables to use, and write the differential of the enthalpy as... 

Most of the chemical reactions run in laboratory courses are to be performed in open systems. This means that there won t be a build-up of pressure and some work will be done by the reacting system on the surroundings or, possibly, by the surroundings on the system. In such cases, the principle of conservation of energy requires that the amount of heat shifted must adjust itself to provide for the small, but significant, amount of this work. A new function, the enthalpy, H, can be defined which is related simply to the heat flow in an open or constant-pressure vessel by the definition, H = E + PV. The amount of heat absorbed (or released) in a constant-pressure process is exactly equal to AH, the increase (or decrease) in H. 

Enthalpy plays a role in constant-pressure processes similar to that of internal energy in constant-volume processes. The heat added to a system in a constant-pressure process is the enthalpy increase of the system. Because U, P, and V (and /, and Lt) are all state functions, H is also a state function. It is extensive. The molar enthalpy, Hm = H/n, is intensive. Dividing Eq. (23) by dTP gives... 

Thus for a mechanically reversible, constant-pressure, nonflow process, the heat transferred equals the enthalpy change of the system. Comparison of the last two equations with Eqs. (2.16) and (2.17) shows that the enthalpy plays a role in constant-pressure processes analogous to the internal energy in constant-volume processes. 

Because the internal energy of an ideal gas is a function of temperature only, both enthalpy and Cp also depend on temperature alone. This is evident from the definition H = U + PV, or H = U + RT for an ideal gas, and from Eq. (2.21). Therefore, just as A U = j CvdT for any process involving an ideal gas, so AH = J CP dT not only for constant-pressure processes but for all finite processes. 

For study of constant pressure processes, it is convenient to define a term called Enthalpy or Heat Content , if, equal to E + PV. Like i , it is impossible to know the absolute value of P[ for a system. But, for convenience, i/for pure elements at atmospheric pressure and 25 °C (298 °K) is taken to be zero. 

While absolute entropy values can now be determined absolute values of Internal Energy and Enthalpy cannot be conceived. For ease of calculation, related especially to metallurgical reactions (constant pressure processes), a suitable reference point of enthalpy is conventionally chosen and that is - for pure elements, the enthalpy is zero when in Standard State . Standard... 

The enthalpy change, dH = T dS + V dp, can be described as dH = dq - -V dp, and for a constant-pressure process, c/p = 0, we have dH = dqp. For a finite state change at constant pressure, qp = AH, that is, the heat transferred is equal to the enthalpy change of the system. This relation is the basis of constant pressure calorimetry, the constant-pressure heat capacity being Cp = dqldT)p. The relationship qp = AH is valid only in the absence of external work, w. When the system does external work, the first law must include dw. Then, the heat transferred to the system under constant-pressure conditions is qp = AH -f w. Thus, if a given chemical reaction has an enthalpy change of -50 kJ mol and does 100 kJ mol" of electrical work, the heat transferred to the system is —50 + 100 = 50 kJ mol". ... 

Enthalpy is useful as a measure of the heat effect of constant-pressure processes. By the first law, dU =bq p dV when pV work is the only work term. At a condition of constant pressure, p dV =... 

On p. 206 it was stated that the heat change under constant-pressure conditions, qp, is equal to the enthalpy change. Therefore, for a constant-pressure process... 

Calculating enthalpy (or energy) change for a constant-pressure process. 

Enthalpy is a state function. A change in enthalpy AH is equal to AE + PAV for a constant-pressure process. 

In Chapter 6 we encountered the first of three laws of thermodynamics, which says that energy can be converted from one form to another, but it cannot be created or destroyed. One measure of these changes is the amount of heat given off or absorbed by a system during a constant-pressure process, which chemists define as a change in enthalpy (A//). 

However, the only heat potential of much interest is the enthalpy, and in fact we could say that the only practical Interest in the enthalpy is that it is a potential for heat in constant pressure processes. As before, if the only work is PAY in a constant pressure process (and remember that at constant P, work is exactly equal to —PAY, not < -PAY), then... 

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). 

Finally, we observed that the enthalpy change of constant pressure processes exactly equals total heat flow ... 

Enthalpy (il) - A thermodynamic function, especially useful when dealing with constant-pressure processes, defined by Ef = + PV, where E is energy, P pressure, and Vvolume. [1]... 

Usually an enthalpy change is a constant-pressure process, changes in work function are for a constant-temperature process, and changes in free energy are for a process occurring at constant pressure and temperature so these equations are usually written... 

For this change in pressure at constant temperature, the enthalpy change is very nearly zero (Section 7.15) and exactly zero if only ideal gases are involved. Thus for practical purposes the AH in Eq. (7.72) is equal to the AH for the constant-pressure process, while the AU refers to the constant-volume transformation. To a good approximation, Eq. (7.72) can be interpreted as... 

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