A History of the Growth of the Steam-Engine

by Robert Henry Thurston

It has now become generally admitted that all forms of energy due to physical forces are mutually convertible with a definite quantivalence; and it is not yet determined that even vital and mental energy do not fall within the same great generalization. This quantivalence is the sole basis of the science of Energetics.

The study of this science has been, up to the present time, principally confined to that portion which comprehends the relations of heat and mechanical energy. In the study of this department of the science, thermo-dynamics, Rankine, Clausius, Thompson, Hirn, and others have acquired great distinction. In the investigations which have been made by these authorities, the methods of transfer of heat and of modification of physical state in gases and vapors, when a change occurs in the form of the energy considered, have been the subjects of especial study.

According to the law of Boyle and Marriotte, the expansion of such fluids follows a law expressed graphically by the hyperbola, and algebraically by the expression PV^x = A, in which, with unchanging temperature, x is equal to 1. One of the first and most evident deductions from the principles of the equivalence of the several forms of energy is that the value of x must increase as the energy expended in expansion increases. This change is very marked with a vapor like steam—which, expanded without doing work, has an exponent less than unity, and which, when doing work by expanding behind a piston, partially condenses, the value of x increases to, in the case of steam, 1.111 according to Rankine, or, probably more correctly, to 1.135 or more, according to Zeuner and Grashof. This fact has an important bearing upon the theory of the steam-engine, and we are indebted to Rankine for the first complete treatise on that theory as thus modified.

Prof. W. J. M. Rankine.

[Prof. Rankine] began his investigations as early as 1849, at which time he proposed his theory of the molecular constitution of matter, now well known as the theory of molecular vortices. He supposes a system of whirling rings or vortices of heat-motion, and bases his philosophy upon that hypothesis, supposing sensible heat to be employed in changing the velocity of the particles, latent heat to be the work of altering the dimensions of the orbits, and considering the effort of each vortex to enlarge its boundaries to be due to centrifugal force. He distinguished between real and apparent specific heat, and showed that the two methods of absorption of heat, in the case of the heating of a fluid, that due to simple increase of temperature and that due to increase of volume, should be distinguished; he proposed, for the latter quantity, the term heat-potential, and for the sum of the two, the name of thermo-dynamic function.

Carnot had stated, a quarter of a century earlier, that the efficiency of a heat-engine is a function of the two limits of temperature between which the machine is worked, and not of the nature of the working substance—an assertion which is quite true where the material does not change its physical state while working. Rankine now deduced that “general equation of thermo-dynamics” which expresses algebraically the relations between heat and mechanical energy, when energy is changing from the one state to the other, in which equation is given, for any assumed change of the fluids, the quantity of heat transformed. He showed that steam in the engine must be partially liquefied by the process of expanding against a resistance, and proved that the total heat of a perfect gas must increase with rise of temperature at a rate proportional to its specific heat under constant pressure.

Rankine, in 1850, showed the inaccuracy of the then accepted value, 0.2669, of the specific heat of air under constant pressure, and calculated its value as 0.24. Three years later, the experiments of Regnault gave the value 0.2379, and Rankine, recalculating it, made it 0.2377. In 1851, Rankine continued his discussion of the subject, and, by his own theory, corroborated Thompson’s law giving the efficiency of a perfect heat-engine as the quotient of the range of working temperature to the temperature of the upper limit, measured from the absolute zero.

During this period, Clausius, the German physicist, was working on the same subject, taking quite a different method, studying the mechanical effects of heat in gases, and deducing, almost simultaneously with Rankine (1850), the general equation which lies at the beginning of the theory of the equivalence of heat and mechanical energy. He found that the probable zero of heat-motion is at such a point that the Carnot function must be approximately the reciprocal of the “absolute” temperature, as measured with the air thermometer, or, stated exactly, that quantity as determined by a perfect gas thermometer. He confirmed Rankine’s conclusion relative to the liquefaction of saturated vapors when expanding against resistance, and, in 1854, adapted Carnot’s principle to the new theory, and showed that his idea of the reversible engine and of the performance of a cycle in testing the changes produced still held good, notwithstanding Carnot’s ignorance of the true nature of heat. Clausius also gave us the extremely important principle: It is impossible for a self-acting machine, unaided, to transfer heat from one body at a low temperature to another having a higher temperature.