Energy U and Enthalpy

The standard enthalpy of formation AHf for a compound is defined as the enthalpy (heat) change for the reaction of formation from the elements under standard conditions, i.e., T = 25°C and P = 1 atm. It either can be measured directly by calorimetric measurements on the direct reaction if possible or may be calculated by Hess s law, which is a consequence of the first 

For a general chemical reaction given by Equation 1.62, one obtains the standard reaction enthalpy by the algebraic stoichiometric sum of the standard enthalpies of formation according to Equation 1.63. 

In Equation 1.63, the stoichiometric factors are positive for products (on the right side of Equation 1.62) and negative for reactants (on the left side). equals for reacting 

Applying the ideal gas law, one obtains A(pV) = Av RT. AV is the change of moles of gas for the reaction. Burning of Imol of CO to CO2 according to Equation 1.60 yields Av = -0.5, which results in 

AfH for dissolved species includes the standard enthalpy of dissolution of the compound, lire formation of 1 mol of HCl in an ideally diluted solution (aq) involves the formation of 1 mol HCl in the gas phase (g) and its dissolution within a large amount of water to a concentration c 0 (Equation 1.65a through c). 

---

Expressions for internal energy, U, and enthalpy, H, in terms of pressure (P), volume (L), and absolute temperature (P) ... 

Some aspects of the kinetic molecular theory (KMT) of ideal gases were outlined in Sidebar 2.7. The simplest form of KMT refers to monatomic ideal gases, for which the internal energy U and enthalpy H=U + PV = U + nRT can be written explicitly as... 

The differential changes in the internal energy u and enthalpy h of an ideal gas can be expressed in terms of the specific heats as... 

In this chapter, a mathematical expression of the First Law will be discussed. The two functions internal energy, U, and enthalpy, H, will figure prominently. In addition, tabulations of standard enthalpy changes of formation, A//0 for a number of compounds, will be given. From such tables it is possible to derive the amount of thermal energy associated with any reaction, as long as all reactants and products are listed. 

Consider an ideal gas composed of diatomic molecules AB. In the limit of absolute zero temperature, all the AB molecules are in their ground states of electronic and nuclear motion, so DqN/ (where is the Avogadro constant and Dq is for the ground electronic state of AB) is the change in the thermodynamic interned energy U and enthalpy H for dissociation of 1 mole of ideal-gas diatomic molecules N/>,Dq = AUl = A//°o for AB(g) A(g) + B(g). 

In fact, heat capacities are commonly not defined in terms of exchanged heat (Qe), but are directly used as derivatives of internal energy U and enthalpy //. The disadvantage here is that, for every side condition (constant volume, constant pressure, constant X, etc.), a different quantity is necessary for the role of heat content. ... 

In equations (4.4.9) and (44.10) we have expressed entropy as a function of U, V and Nk- Since U can be expressed as function of T, V and Nk, entropy can also be expressed as function of T,V and Nk S = S T, V,Nk). (The temperature and volume dependence of the energy U and enthalpy H of each component is obtained by using the empirical values of the heat capacities, as described in Chapter 2.) Since T, V and Nk are directly measurable quantities, it is often more convenient to express thermodynamic variables such as entropy and energy as functions of these variables. 

For calorimetry, heat, Q, is the main measured quantity of interest. Its unit is the joule, J (see Sect. 1.1.2). A number of links between heat and the functions of state, namely heat capacity, Cp, total energy, U and enthalpy, H, were given already in Fig. 1.2 and in the discussion of thermodynamics in Figs. 2.2 to 2.7. 

Classical thermodynamics describes states of equilibrimn and processes that connect states of equilibrium. State functions such as internal energy U and enthalpy H, which are independent of the process path in a change of state, are used. 

Calorimetry is the basic experimental method employed in thennochemistry and thennal physics which enables the measurement of the difference in the energy U or enthalpy //of a system as a result of some process being done on the system. The instrument that is used to measure this energy or enthalpy difference (At/ or AH) is called a calorimeter. In the first section the relationships between the thennodynamic fiinctions and calorunetry are established. The second section gives a general classification of calorimeters in tenns of the principle of operation. The third section describes selected calorimeters used to measure thennodynamic properties such as heat capacity, enthalpies of phase change, reaction, solution and adsorption. 

In most applications, thermodynamics is concerned with five fundamental properties of matter volume (V), pressure (/ ), temperature (T), internal energy (U) and entropy (5). In addition, three derived properties that are combinations of the fundamental properties are commonly encountered. The derived properties are enthalpy (//). Helmholtz free energy (A) and Gibbs free energy ) ... 

Here, h = u + P/p is the enthalpy per unit mass of fluid. Note that the inlet and exit streams include enthalpy (i.e., both internal energy, u, and flow work, P/p), whereas the system energy includes only the internal energy but no P/p flow work (for obvious reasons). If there are only one inlet stream and one exit stream (m, =m0 = m) and the system is at steady state, the energy balance becomes... 

But not all of the heater s energy q goes into raising U. We need some of it to perform pressure-volume work, since the vapour formed on boiling works to push back the external atmosphere. The difference between the internal energy U and the available energy (the enthalpy) is given by... 

Derivation of the expression for the minimum production of S in the systems with constant T and V (volume) differs from the one above only by replacement of enthalpy by internal energy (U) and the Gibbs energy by the Helmholtz energy in the equations. When we set S and P or S and V dissipation turns out to be zero according to the problem statement. In the case of constant U and V or H and P, the interaction with the environment does not hinder the relaxation of the open subsystem toward the state max Sos. 

The molar energies of formation U and enthalpies H for a given explosive with the composition CaHbNcOd can be connected as follows ... 

Enthalpy (H) An extensive property of a substance that can be used to obtain the heat absorbed or released by a chemical reaction or physical change at constant pressure. It is defined as the sum of the internal energy (U) and the product of the pressure and the volume of the system (PV) H = U + PV. 

Note that in the present context no distinction need be made between the energy U and the enthalpy H, nor between the Helmholtz free energy F and the Gibbs free energy G. In the following chapters we shall use the Gibbs free energy. 

The internal energy U and the enthalpy // of a closed homogeneous system of constant composition are described by the internal state variables p, V and T which are related to each other via the equation of state. 

Since both the energy U and the term pV are constant, we have U + pV = H and thus the enthalpy in the Gay - Lussac process is constant. Conversely, we can state that for an ideal gas, when we set pF = C as a constant, then the energy remains constant. 

The internal energy U, the enthalpy H, the free internal energy F, and the free enthalpy G, must be at a minimum for a system to be at equilibrium. This is comparable to a me-... 

These equations show that for an ideal gas the internal energy u, the enthalpy h, and the specific heat capacities at constant pressure Cp and at constant volume are only functions of the temperature and independent of pressure or volume. On the other hand, the specific entropy (s), the specific Gibbs energy (g), and the specific Helmholtz energy (o) are functions of temperature and pressure or volume even for an ideal gas. 

The specific internal energy u and the specific enthalpy h are related by h = u + Pv... 

We cannot measure the absolute internal energy U or enthalpy H because the zero of energy is arbitrary. As a result, we are usually only interested in determining changes in these properties (At/ and A.H) during a process. However, it is possible to determine the absolute entropy of a substance. This is because of the third law of thermodynamics, which states that the entropy of a pure substance in its thermodynamically most stable form is zero at the absolute zero of temperature, independent of pressure. For the vast majority of substances, the thermodynamically most stable form at 0 K is a perfect crystal. An important exception is helium, which remains liquid, due to its large quantum zero-point motion, at 0 K for pressures below about 10 bar. 

---