Combined first and second law statement

The treatments that are concerned in more detail with the nature of the adsorbed layer make use of the general thermodynamic framework of the derivation of the Gibbs equation (Section III-5B) but differ in the handling of the electrochemical potential and the surface excess of the ionic species [114-117]. The derivation given here is after that of Grahame and Whitney [117]. Equation III-76 gives the combined first- and second-law statements for the surface excess quantities... 

THE COMBINED FIRST AND SECOND LAW STATEMENT REVERSIBLE WORK... 

The combined first and second law statement allows us to calculate the reversible work for any process, actual or hypothetical. It also leads to the definitions of several useful convenience functions. 

We can begin with Equation (7.1) as a statement of the combined first and second laws, which were rearranged to... 

Equation (1.75) is a mathematical statement of the second law of thermodynamics for reversible processes. The introduction of the integrating factor for Sq causes the thermal energy to be split into an extensive factor. S and an intensive factor T. Introducing Eq. (1.75) into Eq. (1.56) yields the combined first and second laws... 

Then (Sq/T) becomes a state function called entropy and T the absolute temperature. As a state function, entropy is path-independent. Eqn (1.25) is a mathematical statement of the second law of thermodynamics. The introduction of the integrating factor for 8q causes the thermal energy to be split into an extensive factor S and an intensive factor T. Clausius defined the entropy with the integrating factor of the inverse of absolute temperature in T 8q) = dS. Similarly, integrating factor 1/P in IP 6W) = dV leads to exact differential dV, which is formulated by Clapeyron in 1834. Introducing Eqn (1.25) into the first law of thermodynamics dU =8q + yields the combined first and second laws of thermodynamics... 

Perhaps the most important, concepts of the axiomatic foundation of ther modynamics are the ones referred to as the First and Second Laws dealing with the internal energy U and the entropy S. They are essentially statements dealing with energy conservation and the transformation of one form of energy (e.g., work) into another one (e.g., heat). If combined, the First and Second Laws give rise to the so-called Gibbs fundamental equation... 

The first and second laws of thermodynamics are the basis on which thermodynamic relationships are derived. The two laws, represented by Equations 1.1 and 1.2, are combined in the following statement ... 

The functions A and G combine together the statements of the First and Second Laws and are of fundamental importance. 

From the combined statement of the first and second laws of thermodynamics we can write that the change in internal energy, dE, is... 

PI 1.1 The first of the four fundamental equations of Gibbs equation (11.10) is obtained by combining equation (11.6), the statement of the First Law applied to the system, with equation (11.7), the Second Law statement for a reversible process, again applied to the system, and equation (11.8) that calculates reversible pressure-volume work. Start with equation (11.10) and the defining equations for H, A, and G equations (11.1), (11.2), and (11.3), and derive the other Gibbs equations equations (11.11), (11.12), and (11.13). ... 

A second Pfaffian differential of interest to us now is the one for the differential quantity of heat, 8c/KV, associated with a reversible process.11 We obtain it by combining equation (1.47) with the first law statement (equation (2.4) that relates U, vv, and q... 

With the entropy term introduced, it is possible to make a combined statement of the first and the second laws. To do this, one may consider an infinitesimal change of state of a closed system. For this, the first law gives... 

It has now been demonstrated how considerations of work and heat changes in cyclical processes combined with a statement of the Second Law lead to the development of a quantity that can distinguish possible from impossible processes under certain conditions. The next step is to combine this with a statement of the First Law to get our first look at a fundamental equation . 

The famous Clausius statement is as follows It is impossible to construct a device to work in a cyclic process whose sole effect is the transfer of heat from a body at a lower temperature to a body at a higher temperature. Clausius also stated the first and the second laws of thermodynamics combined together as The energy of the universe is constant, and The entropy of the universe tends toward a maximum. ... 

In 1808 Jean Louis Gay-Lussac (1778-1850) summarized the results of experiments of others and a few of his own and discovered the law of combining volumes of gases. He realized that volumes of gases could only he compared if their pressures and temperatures were equal. (The first statement is Boyle s Law the second is sometimes called Charles Law after the first discoverer or Gay-Lussac s Law after the person who first published it.) Thus, equal volumes of ammonia (NH3) and muriatic acid (HCl) combine perfectly to form a solid salt one volume of nitrogen and one volume of oxygen form two volumes of nitrous gas (NO). One volume of nitrogen and three volumes of hydrogen form two volumes of ammonia. 

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