9.5.1 Energy at the Microscopic Level

FIGURE 9.22 shows two different perspectives of an object. In Figure 9.22a you see an object of mass m moving as a whole with velocity $v_{obj}$ . As a consequence of its motion, the object has macroscopic kinetic energy $K_{macro} = \frac{1}{2} m v_{obj}^{2}$ .

The figure labeled (“a”) illustrates the macroscopic motion of a system as a whole.

The figure labeled (b) illustrates the microscopic motion of atoms inside an object.

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NOTE You recognize the prefix micro, meaning “small.” You may not be familiar with macro, which means “large.” Everyday objects, which consist of vast numbers of particle-like atoms, are macroscopic objects.

As you know, this macroscopic object is made up of atoms. But the atoms are not sitting quietly at rest. Instead, as Figure 9.22b shows, each of these atoms is jiggling about and has kinetic energy. As the atoms move, they stretch and compress the spring-like bonds between them. We’ll study potential energy in Chapter 10, but you’ll recall from the energy overview at the beginning of this chapter that potential energy is stored energy. Stretched and compressed springs store energy, so the bonds have potential energy.

The energy of one atom is exceedingly small, but there are enormous numbers of atoms in a macroscopic object. As all these atoms undergo random motion, the combined microscopic kinetic and potential energy of the atoms—the energy of the jiggling atoms and stretching bonds—is called the thermal energy of the system, $E_{th}$ . This energy is distinct from the macroscopic energy of the object as a whole. Thermal energy is hidden from view in our macrophysics perspective, but it is quite real. We will discover later, when we reach thermodynamics, that the thermal energy is related to the temperature of the system. Raising the temperature causes the atoms to move faster and the bonds to stretch more, giving the system more thermal energy.

NOTE The microscopic energy of atoms is not called “heat.” As was mentioned earlier, heat is a process, similar to work, for transferring energy between the system and the environment. We’ll have a lot more to say about heat in future chapters.

With the inclusion of thermal energy, a system can have both macroscopic kinetic energy and thermal energy: $E_{sys} = K + E_{th}$ . With this, the energy principle becomes

Δ E_{sys} = Δ K + Δ E_{th} = W_{ext}

(9.26)

where $W_{ext}$ is the work due to external forces acting on the object. Work done on the system might increase the system’s kinetic energy, its thermal energy, or both. Or, in the absence of work, kinetic energy can be transformed into thermal energy as long as the total energy change is zero. Recognizing thermal energy greatly expands the range of problems we can analyze with the energy principle.

NOTE The introduction of thermal energy requires us to move beyond the simple particle model. A particle has no internal structure and cannot have thermal energy. Macroscopic objects that have thermal energy are extended objects.