Functions in Thermodynamics

Themodynamic State Functions In thermodynamics, the state functions include the internal energy, U enthalpy, H and Helmholtz and Gibbs free energies, A and G, respectively, defined as follows ... 

Thus q and w are different from most other functions in thermodynamics. 

Inasmuch as the same function T of an empirical temperature scale serves as an integrating denominator of specific properties of the system under study, it is called the absolute temperature (function ) in thermodynamics and may be used as a universal function for measuring temperature. 

Examples of thermodynamic calculations are discussed by Kelley 181 y 18Sy 184) (italic numbers in parentheses refer to the bibliography on page 227) in his pioneer bulletins on practical applications of thermodynamics. Other examples are detailed by Brewer and coworkers (36), More recently. Margrave (333) has presented the advantages of the free energy function in thermodynamic calculations. In the hydrocarbon field, representative papers by Rossini and coworkers (103, 189y 339) demonstrate the value of thermodynamics for the petroleum industry. 

The most important use of state functions in thermodynamics is to describe changes. We describe the difference in any quantity, X, as... 

First of all, we examine the partition function Z — an important function in thermodynamics and statistics, and calculate the free energy of the system according to the formula... 

In this example, there was no difficulty in obtaining an expression for the difference between dz/dx)y and (9z/9x) , because we had the formula to represent the mathematical function. In thermodynamics, it is unusual to have a functional form. More commonly we have measured values for partial derivatives and require a separate means for computing the difference between partial derivatives. 

State function In thermodynamics a variable is a state function if, when all the thermodynamic variables are specified, it has a unique value. As a result, the change in any state function in a reversible cyclic process must be zero. 

The ideal solutions are characterized by zero excess thermodynamic functions. In thermodynamics, ideal solutions are often characterized by their excess entropy and enthalpy. Note that to obtain these, we need to assume differentiability of (4.91) with respect to temperature. This assumption is still quite weaker than the requirement that (4.91) be valid at all T and P. 

Jacobians, which are simply functional determinants, have long been used to simplify derivations of functions in thermodynamics (Crawford, 1950 Carroll, 1965). Our interest in Jacobian transformation is for its great simplicity and usefulness in transformation of the various derivations of the Legendre transformation of thermodynamic functions. Without the Jacobian transformation, the interrelation between the derivations of Legendre transformation become very complicated. 

Our treatment of engines will suggest a new state function, called entropy. Using its initial definition as a start, we will derive some equations that allow us to calculate the entropy changes for various processes. After considering a different way of defining entropy, we will state the third law of thermodynamics, which makes entropy a unique state function in thermodynamics. Finally, we will consider entropy changes for chemical reactions. 

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