Page:International Library of Technology, Volume 93.djvu/72

 77. When air is compressed adiabatically, the heat that is added to it by the work of compressing it cannot escape, and consequently the air will have a higher temperature and pressure than when compressed isothermally. This being true, it is evident that the air does not follow a curve having $$p v =$$ a constant as its equation. Instead, the equation of adiabatic changes of state is $$pv^k =$$ a constant. That is, the product of the pressure and the kth power of the volume is constant, in which k is the ratio of the specific heat at constant pressure to that at constant volume. As stated in Art. 62, k = 1.405 for dry air.

78. Suppose that 10 cubic feet of air at a pressure of 10 pounds is compressed adiabatically to a volume of 2 cubic feet. The compression maybe represented by a diagram, Fig. 14, as in the case of isothermal compression, Fig. 13. The original state of the air is represented by the point K, and at that point $$p v^1.405$$ = a constant. To find the value of this constant, logarithms must be used. Thus, $$\log p + 1.405 (\log v) =$$ log of constant, or $$\log 10+ 1.405 (\log 10) = 1 + 1.405 \times 1 = 1 + 1.405 = 2.405 =$$ log of constant Hence, the constant is 254.1. Now, at every other stage of the compression, the product of the pressure and the kth power of the volume must equal 254.1. Let the volume be com- pressed to 9 cubic feet. Then, $$pv^{1.405} = 254.1$$, or $$p (9)^{1.405}$$