[Footnote 1:  I use material terms because they add to simplicity of expression and notwithstanding the fact that heat is vibration.]

Thirteen cubic feet of free air at normal temperature and barometric pressure weigh about one pound.  We have seen that 116 degrees of heat have been liberated at half stroke.  The gauge pressure at this point reaches 24 pounds.  According to Mariotte’s law, “The temperature remaining constant, the volume varies inversely as the pressure,” we should have 15 pounds gauge pressure.  The difference, 9 pounds, represents the effect of the heat of compression in increasing the relative volume of the air.

[Illustration:  Fig. 1.:  Curves of compression ILLUSTRATEDIN volumes, pressures, and temperatures.]

The specific heat of air under constant pressure being 0.238, we have 0.238 x 116 = 27.6 heat units produced by compressing one pound or thirteen cubic feet of free air into one-half its volume. 27.6 x 772 (Joule’s equivalent) = 21,307 foot pounds.  We know that 33,000 foot pounds is one horse power, and we see how easily about two-thirds of a horse power in heat units may be produced and lost in compressing one pound of air.  I would mention here that exactly this same loss is suffered when compressed air does work in an engine and is expanded down to its original pressure.  In other words, the heat of compression and the cold of expansion are in degree equal.

Experiments made by M. Regnault and others on the influence of heat on pressures and volumes of gases have enabled us to fix the absolute zero of temperature as -461 degrees Fahrenheit.  This point, 461 degrees below zero, is the theoretical point at which a volume of air is reduced to nothing.  The volume of air at different temperatures is in proportion to the absolute temperature, and on this basis Box gives us the following table: 

TABLE l.—­OF THE VOLUME AND WEIGHT OF DRY AIR AT DIFFERENT TEMPERATURES UNDER A CONSTANT ATMOSPHERIC PRESSURE OF 29.92 INCHES OF MERCURY IN THE BAROMETER (ONE ATMOSPHERE), THE VOLUME AT 32 deg.  FAHRENHEIT BEING 1.

  Temperature Volume in Weight of a
  in degrees. cubic feet. cubic foot in lb.
       32 1.000 0.0807
       42 1.020 0.0791
       52 1.041 0.0776
       62 1.061 0.0761
       72 1.082 0.0747
       82 1.102 0.0733
       92 1.122 0.0720
      102 1.143 0.0707
      112 1.163 0.0694
      122 1.184 0.0682
      132 1.204 0.0671
      142 1.224 0.0660
      152 1.245 0.0649
      162 1.265 0.0638
      172 1.285 0.0628
      182 1.306 0.0618