Modern Engineering Thermodynamics

116 CHAPTER 4: The First Law of Thermodynamics and Energy Transport Mechanisms
Table 4.2 Generalized Forces and Generalized Displacements
Work Mode Generalized Force F Generalized Displacement dχ
Moving system boundary p (pressure) dV (volume)
Shaft T (torque) dθ (angular displacement)
Elastic −σ (stress) Vdε (volume)
Surface tension −σ s (surface tension) dA (surface area)
Example 4.7 shows that it would take all of the surface tension energy stored in nearly 2 million 5 cm diameter
soap bubbles to raise the temperature of one pound-mass of water by one degree Fahrenheit.
Notice that, in each of the four cases of classical mechanical work, the work differential dW was given by the
product of what we can call a generalized force F and a generalized displacement dχ; that is,
dW = Fdχ (4.44)
where F and dχ for each of the four classical mechanical work modes are identified in Table 4.2. In Eq. (4.44),
the scalar or dot product is implied if F and dχ are vectors.
The application of these work modes may change the thermodynamic state of the system and thus may produce
a change in the system’s thermodynamic properties. Finally, note that the generalized forces are all intensive
properties, whereas the generalized displacements are all extensive properties.
We can generalize the work concept to nonmechanical systems by including any work mode given by Eq. (4.44)
when the generalized force F is an intensive property forcing function and the generalized displacement dχ is an
extensive property response function. We are now in a position to analyze the remaining work mode energy
transport mechanisms.
4.7 NONMECHANICAL WORK MODES OF ENERGY TRANSPORT
Of the wide variety of nonmechanical work modes available, the following five are of significant engineering
value:
1. Electrical current flow.
2. Electrical polarization.
3. Magnetic.
4. Chemical.
5. Mechanochemical.
Materials are electrically classified as conductors, nonconductors (dielectrics or insulators), and semiconductors. A pure
conductor is a substance that has mobile charges (electrons) free to move in an applied electric field. They constitute the
flow of electrical current. Pure nonconductors have no free electrons whatsoever, and a semiconductor is a material that
behaves as a dielectric (nonconductor) at low temperatures but becomes conducting at higher temperatures.
As an electric field E is applied to a pure conductor, the free electrons migrate to the conductor’s outer surface,
where they create their own electric field, which opposes the applied field. As more and more electrons reach
the outer surface, the electric field inside the object grows weaker and weaker, eventually vanishing altogether.
At equilibrium, there is no electric field within a pure conductor.
A pure nonconductor has no free electrons with which to neutralize the applied electric field. The externally
applied field therefore acts on the internal molecules, and normally nonpolar molecules become polar and
develop electric dipoles. Some molecules are naturally polar in the absence of an electric field (e.g., water). The
applied electric field rotates and aligns the newly created or naturally polar molecules. Complete alignment is
normally prevented by molecular vibrations. But, when the applied field is strong enough to overcome the
vibration randomizing effects and further increases in field strength have no effect on the material, the material
is said to be saturated by the applied field. The process of electric dipole creation, rotation, and alignment in an
applied electric field is known as dielectric polarization.
Therefore, two work modes arise from the application of an electric field to a material. The first is the work associated
with the free electron (current) flow, and the second is the work associated with dielectric polarization.
For a pure conductor, the polarization work is always zero; and for a pure nonconductor, the current flow work
is always zero. We always treat these as separate work modes.