A History of the Growth of the Steam-Engine

*The name of thermo dynamic function*

The

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

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.

[Illustration: Prof. W. J. M. Rankine.]

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.