Page:International Library of Technology, Volume 93.djvu/74

curve. Fig. 15

shows such a comparison. The curves AD

and AG are the isothermal- and adiabatic-expansion curves, respectively, of same volume of air at the same initial pressure. As shown, the adiabatic curve lies below the isothermal at all points. The points B, C, D and E, F, G are located by the methods described in connection with Figs. 13 and 14.

80. In actual work, as, for example, in the case of the gas engine, where a quantity of heated gases expands in the cylinder and drives the piston be- fore it, the expansion is neither isothermal nor adiabatic; that is, the curve of the expansion follows neither the law $pv=$ a con- stant nor $pv^{k}=$ a constant. The reason for this may be readily explained. In order to keep the temperature of an expanding gas constant, heat must be added during the expansion, and, as this is not done, the expansion is not isothermal. Furthermore, the cylinder is of metal, which conducts heat very readily. Hence, there is considerable heat lost by conduction and radiation, and so the expansion cannot be adiabatic.

In ordinary practice, it is found that the actual curve of expansion of a gas lies somewhere between the isothermal and the adiabatic. Thus, in Fig. 15, if AD and AG represent the true isothermal- and adiabatic-expansion curves of the given amount of air, the actual-expansion curve will be represented by some other line, as AH, lying between AD and AG. The equation of this curve is $pv^{n}=$ a constant, in which n has a value that lies between 1 and 1.405, varying according to the different conditions under which the engine works.

As in the cases of isothermal and adiabatic expansion and compression, the expansion, according to the law $pv^{n}=$ a constant, will follow the same curve as in compression, all conditions being the same.