{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Schieber_and_Depablo_Chapter_3 - Chapter 3 Generalized...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 3 Generalized Thermodynamic Potentials A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown (for the special attention of those who are skeptics on principle). – Albert Einstein 1 From the postulates in Chapter 2, we have already seen that from U ( S , V , N 1 , ... , N m ) or S ( U , V , N 1 , ... , N m ) we can derive all thermodynamic informa- tion about a system. For example, we can find mechanical or thermal equations of state. However, we also know that it is sometimes convenient to use other in- dependent variables besides entropy and volume. For example, when we perform an experiment at room temperature open to the atmosphere, we are manipulating temperature and pressure, not entropy and volume. In this case, the more natural independent variables are T and P . Then, the question arises: Is there a function of ( T,P,N 1 ,...,N m ) that contains complete thermodynamic information? In other words, is there some function, say G ( T,P,N 1 ,...,N m ) from which we could derive all the equations of state? It turns out that such functions do exist, and that they are useful for solving practical problems. 1 Albert Einstein: Philosopher-Scientist, p.33, ed. by P. A. Schilpp, (Cambridge U.P., London, 1970) 61
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
62 CHAPTER 3. GENERALIZED THERMODYNAMIC POTENTIALS In the first section we show how to derive such a function for any complete set of independent variables using Legendre Transforms. In this book we introduce three widely used potentials: the enthalpy H ( S,P,N 1 ,...,N m ), the Helmholtz potential F ( T,V,N 1 ,...,N m ), and the Gibbs free energy G ( T,P,N 1 ,...,N m ). These func- tions that contain complete thermodynamic information using independent variables besides S,V and N 1 ,...,N m are called generalized thermodynamic potentials . These quantities are essential for engineering or applied thermodynamics. For example, we already know that an isolated system attains equilibrium when the entropy is maximized. However, a system in contact with a thermal reservoir at- tains equilibrium when the Helmholtz potential F is minimized. We show below (Examples 3.2.1 and 3.2.2), that the work necessary to compress any gas isother- mally is just the change in F ( T,V,N ). In a fuel cell, G ( T,P,N ) is important. Or, in the open (flowing) systems considered in Chapter 5, we see that another such function (called enthalpy) is also important. In other words, we need not consider the entropy of the reservoir explicitly to find equilibrium. We will also see in later chapters, that the enthalpy H ( S,P,N ) plays an important role in flowing systems and in applications.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern