Thermodynamics

Thermodynamics is a modern branch of the science of heat, and is founded chiefly upon the deductions of Joule, Carnot, and other workers in the same field. Two fundamental principles underlie this science. The first law of thermodynamics states that when heat is used in doing work, the work done is exactly the equivalent of the heat expended, and when work is done to produce heat, the heat produced is exactly proportional to the work done. This follows from the law of the conservation of energy, when it is accepted that heat is a form of energy. But only in modern times has heat been universally regarded as energy; it is true that some of the early Greek philosophers considered it as in some way connected with motion, and speculations on the dynamical theory of heat were rife in the time of Bacon, but by far the greater number of scientists held the opinion that heat was a sort of elastic fluid permeating all bodies - bodies becoming hotter as more of this fluid or caloric was given to them, and colder as it was taken away. Caloric, like matter, was indestructible and uncreatable, and it was finally decided about a century ago that it was weightless, though much doubt had previously existed on the subject. But everything could not be satisfactorily explained by the caloric theory. Friction was known to generate heat, and when a body was ground to powder it was supposed to lose some caloric, which raised its temperature, the heat capacity of the powder being therefore assumed to be less than that of the original solid. Rumford proved the error of this assumption by actual experiment in 1798, but did not succeed in convincing the calorists. He concluded that motion was at the root of the matter, and Davy followed witb similar reasoning. In 1840, however, Joule experimentally determined the numerical relation between work spent and heat generated, and stated that 772 foot-pounds of work were capable of raising one pound of water through one degree Fahrenheit. This may be written W = 772 H. With different units the number will alter, and in general terms the equation is written W = J H, J being called the mechanical equivalent of heat. Experiments were also made on the reverse problem - the determination of the amount of work done by the expenditure of a certain amount of heat - and Hirn showed the connection between the heat given out by the boiler of an ordinary steam-engine and the work done in the same time, allowing for the heat received by the condenser and that lost by radiation, etc. Almost countless experiments have been made to determine the true valne of J, the names including Joule, Faire, Hirn, Weber, and workers at the present time, an enormous number of direct and indirect methods having been employed.

The second law of thermodynamics is expressed by Clausius thus :- It is impossible for a self-acting machine, unaided by an external agency, to convey heat from one body to another at a higher temperature;" while Lord Kelvin states that "it is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects." We may take any two substances at different temperatures and theoretically allow the pair to do work. A heat engine is therefore imagined - the body at the higher temperatnre being regarded as the furnace, and that at the lower as the condenser; the work done is equivalent to the difference of the heat obtained from the furnace and given to the condenser. Heat cannot of itself pass from a colder to a warmer body, but, if work be done, then heat can be withdrawn from the cooler condenser, and given up to the hotter source. This involves the conception of a reversible engine, and considerations of such a machine were first investigated by Carnot.

If a substance be allowed to expand against pressure, it does external work, but it does not follow that this external work is at all the equivalent of the heat expended; internal work may also have been done in overcoming molecular attraction, surface tension, electrical forces, and so on. But we may take our substance through a cycle of operations and finish with it in exactly the same state as it was at starting, in which case we get rid of the unknown quantities included under the name of internal work. In the final enumeration of effects, whatever the external work may have been, the internal work cancels out.

Let us take a working substance and subject it to certain alterations of temperatnre, pressure, and volume. If we take distances measured in the direction O V to represent volumes and those in the direction 0 P to represent pressures, then the state of a substance represented by A is such that its volume is O a and its pressure a A. Suppose this substance is contained in a cylinder, and that the volume is increased by allowing the piston to rise. Imagine further that thecylinder is in such a position that no conduction of heat can take place. No heat is allowed to enter or leave the substance, while its volume increases to O b. Its path may be represented by the line A B, which is known as an adiabatic curve. During this process, as the substance has done external work represented by the area a A B b on the diagram and no heat has entered it, its temperature must have fallen.

Now remove the cylinder from its non-conducting position, place it in contact with a body at its present temperature, and compress the substance until its volume is O c. Its condition is now represented by the point C. Through this operation its temperature has been kept constant; hence B C is called an isothermal curve. Work, represented by, C B b c, has been done on the substance, and so heat must have been given out to the body, called the condenser, with which it has been in contact.

Again place the substance in its non-conducting position, and force in the piston. The varying condition of the substance is shown by another adiabatic curve, C D. Work (D C c d) is done on the substance; no heat can leave it, and so its temperature rises. Continue this process till the temperature is the same as at the beginning of the cycle, and the point reached is D. Now put the cylinder in communication with the source of heat, keep its temperature constant, and let it expand isothermally till it reaches A, its starting-point. It does work (D A a d), and takes up heat from the source. Summing up the results of these four operations, we find a balance of work done by the substance represented by the area D A B C, while an amount of heat (H) has been taken from the source at a temperature (T), a quantity (h) having been given up to the condenser at a lower temperature (t). Carnot's first belief was that H and h were equal, but this is disproved by the dynamical theory of heat. In reality the work D A B C is the exact equivalent of H--h. This whole circle of operations is reversible. We can cause the substance to undergo exact1y the reverse operations - take in heat h at t, and give out H at T; while work equal to D A B C is done on the body. A reversible engine is one in which the working substance can be made to go through a reversible cycle - to pass into its initial or final state alternately, and Carnot proved that a reversible engine must have the highest possible efficiency, efficiency being defined as the ratio W/H, where W is the work done by the engine in one cycle, and H as before is the heat received by the substance at the higher temperature. The efficiency must therefore depend only on T and t, and be independent of the substance used. Since W/H is the same as H-h/H, we see that in the consideration of efficiency we are dealing with a connection between the quantities of heat H, h, and the temperature T, t. Upon this connection Lord Kelvin in 1848 based a scale of absolute temperature. An absolute zero was determined, independent of the nature of the working substance. This absolute zero of the thermodynamic scale is practically the same as that of a thermometer based upon the behaviour of a perfect gas.

The second law of thermodynamics may be expressed mathematically as an equation between the heat and entropy (q.v.) of a substance. For further information on entropy and more extensive considerations of the deductions arrived at in thermodynamics, the reader is referred to such books as Maxwell's Theory of Heat, a larger work by Preston, and similar literature.