Energy

   A property that will occur in just about every chapter of the following text is the energy, E. Everyone uses the term “energy” in everyday language, but in science it has a precise meaning, a meaning that we shall draw on throughout the text.

  Energy is the capacity to do work. A fully wound spring can do more work than a half-wound spring (that is, it can raise a weight through a greater height or move a greater weight through a given height). A hot object has the potential for doing more work than the same object when it is cool and therefore has a higher energy.

  The SI unit of energy is the joule (J), named after the nineteenth-century scientist James Joule, who helped to establish the concept of energy (see Chapter 1). It is defined as

1 J = 1 kg m² s^-2

A joule is quite a small unit, and in chemistry we often deal with energies of the order of kilojoules (1 kJ = 103 J).

There are two contributions to the total energy of a collection of particles. The kinetic energy, EK, is the energy of a body due to its motion. For a body of mass m moving at a speed v,

EK = 1⁄2mv²          (F.1)

That is, a heavy object moving at the same speed as a light object has a higher kinetic energy, and doubling the speed of any object increases its kinetic energy by a factor of 4. A ball of mass 1 kg traveling at 1 m s^-1 has a kinetic energy of 0.5 J.

The potential energy, EP, of a body is the energy it possesses due to its position. The precise dependence on position depends on the type of force acting on the body. For a body of mass m on the surface of the Earth, the potential energy depends on its height, h, above the surface as

EP= mgh                (F.2)

where g is a constant known as the acceleration of free fall, which is close to 9.81 m s^-2 at sea level. Thus, doubling the height of an object above the ground doubles its potential energy. Equation F.2 is based on the convention of taking the potential energy to be zero at sea level. A ball of mass 1.0 kg at 1.0 m above the surface of the Earth has a potential energy of 9.8 J. Another type of potential energy is that of one electric charge in the vicinity of another electric charge.

As we shall see as the text develops, most contributions to the potential energy that we need to consider in chemistry are due to this Coulombic interaction. The total energy, E, of a body is the sum of its kinetic and potential energies:

E =E_K + E_P         (F.3)

Provided no external forces are acting on the body, its total energy is constant. This remark is elevated to a central statement of classical physics known as the law of the conservation of energy. Potential and kinetic energy may be freely interchanged: for instance, a falling ball loses potential energy but gains kinetic energy as it accelerates, but its total energy remains constant provided the body is isolated from external influences.