examples could be provided that enlarge on the same idea.
When work is done to compress a spring, energy is stored within the spring. When a battery is charged, the energy stored within it is increased. And when a gas (or liquid) initially
at an equilibrium state in a closed, insulated vessel is stirred vigorously and allowed to come
to a final equilibrium state, the energy of the gas is increased in the process. In each of these
examples the change in system energy cannot be attributed to changes in the system’s overall
kinetic or gravitational potential energy as given by Eqs. 2.5 and 2.10, respectively.
The change in energy can be accounted for in terms of internal energy, as considered next.
In engineering thermodynamics the change in the total energy of a system is considered
to be made up of three macroscopic contributions. One is the change in kinetic energy, associated with the motion of the system as a whole relative to an external coordinate frame.
Another is the change in gravitational potential energy, associated with the position of the
system as a whole in the earth’s gravitational field. All other energy changes are lumped together in the internal energy of the system. Like kinetic energy and gravitational potential
energy, internal energy is an extensive property of the system, as is the total energy.
Internal energy is represented by the symbol U, and the change in internal energy in a
process is U2 U1. The specific internal energy is symbolized by u or , respectively, depending on whether it is expressed on a unit mass or per mole basis.
The change in the total energy of a system is
All quantities in are expressed in terms of the energy units previously introduced.
The identification of internal energy as a macroscopic form of energy is a significant step
in the present development, for it sets the concept of energy in thermodynamics apart from
that of mechanics. In Chap. 3 we will learn how to evaluate changes in internal energy for
practically important cases involving gases, liquids, and solids by using empirical data.
To further our understanding of internal energy, consider a system we will often encounter
in subsequent sections of the book, a system consisting of a gas contained in a tank. Let us
develop a microscopic interpretation of internal energy by thinking of the energy attributed
to the motions and configurations of the individual molecules, atoms, and subatomic particles making up the matter in the system. Gas molecules move about, encountering other molecules or the walls of the container. Part of the internal energy of the gas is the translational
kinetic energy of the molecules. Other contributions to the internal energy include the kinetic
energy due to rotation of the molecules relative to their centers of mass and the kinetic energy
associated with vibrational motions within the molecules. In addition, energy is stored in the
chemical bonds between the atoms that make up the molecules. Energy storage on the atomic
level includes energy associated with electron orbital states, nuclear spin, and binding forces
in the nucleus. In dense gases, liquids, and solids, intermolecular forces play an important
role in affecting the internal energy
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