Fig. 3
By the application of heat energy, the temperature of the water in the vessel A is raised to a point say 100° F. above that of B, and steadily maintained at that point. It is assumed that B is also kept at the constant lower temperature. In these circumstances, a transmission of heat energy takes place from A to B through the metallic bar. When the steady temperature condition is reached, the transmission will be continuous and uniform; the rate at which it is carried out will be determined by the length of the bar, by the material of which it is composed, and by the temperature difference maintained between its ends. Now what has really happened is that by a combination of phenomena the bar has been converted into a machine for the transmission of heat energy. A full description of these phenomena is, in reality, the description of this machine, and vice versa. Let us, therefore, now try to outline some of these phenomena.
The first feature of note is the gradient of temperature which exists between the ends of the bar. Further research is necessary regarding the real nature of this gradient—it appears to differ greatly in different materials—but the existence of such a gradient is one of the main features of the energy machine, one of the essential conditions of the transmission process.
Another feature is that of the expansive motion of the bar itself. The expansion of the bar due to the heating varies in value along its length, from a maximum at the hot end to a minimum at the cool end. The expansion, also, is the evidence of a transformation of energy. The bar has been constrained into its new form against the action of the internal molecular or cohesive forces of its material (§ [16]). The energy employed and transformed in producing the expansion is a part of the original heat energy applied to the bar, and before any transmission of this heat energy takes place between its extreme ends, a definite modicum of the applied energy has to be completely transformed for the sole purpose of producing this distortive movement or expansion against cohesion. This preliminary straining of the bar is, in fact, a part of the process of building up or constituting the energy transmission machine, and must be completely carried out before any transmission can take place. It is clear, then, that concurrent with the gradient of temperature, there also exists, along the bar, what might be termed a gradient of energy stored against cohesion, and that both are characteristic and essential features of this particular energy machine. A point of some importance to note is the permanency of these features. Once the machine has been constituted with a constant temperature difference, the transmission of energy will take place continuously and at a uniform rate. But no further transformation against cohesion takes place; no further expenditure of energy against the internal forces of the material is necessary. Neglecting certain losses due to possible external conditions, the whole energy applied to the machine at the one end is transmitted in its entirety to the other, without influencing in any way either the temperature or the energy gradient.
Such is the general constitution of this machine for energy transmission. Its material foundation is, indeed, the metallic bar, but the temperature and energy gradients may be termed the true determining factors of its operation. As already indicated, the magnitude of the transformation is dependent on the temperature difference between the ends of the bar. But this applies only within certain limits. With respect to the cool end, the temperature may be as low as we please—so far as we know, the limit is absolute zero of temperature; but with the hot end, the case is entirely different, because here the limit is very strictly imposed by the melting-point of the material of the bar. When this melting temperature is attained, the melting of the bar indicates, simply, that the heat energy stored or transformed against the cohesive forces of the material has reached its limiting value; change of state of the material is taking place, and the machine is thereby being destroyed.
It is evident, then, that the energy which is actually being transmitted has itself no effect whatever in restricting the action or scope of the transmission machine. It is, in reality, the residual energy stored against the cohesive forces which imposes the limits on the working. It is the maximum energy which can be transformed in the field of the cohesive forces of the material which determines the power of that material as a transmitting agent. This maximum will, of course, be different for different materials according to their physical constitution. It is attained in this machine in each case when melting of the bar takes place.
28. Some Phenomena of Transmission Processes—Transmission by Flexible Band or Cord
This method is often adopted when energy of motion, or mechanical energy, is required to be transmitted from one point to another. For illustration, consider the case of two parallel spindles or shafts, A and B ([Fig. 4]), each having a pulley securely keyed upon it. Spindle A is connected to a source of of mechanical energy, and it is desired to transmit this energy across the intervening space to spindle B.