Machinery's Handbook, 31st Edition
2814 WORK REQUIRED IN COMPRESSION OF AIR the volume is inversely proportional to the absolute pressure. Theoretically, air (as well as other gases) can be expanded or compressed according to different laws. Adiabatic Expansion or Compression takes place when the air is expanded or com pressed without transmission of heat to or from it, as, for example, if the air could be expanded or compressed in a cylinder of an absolutely nonconducting material. Let: P 1 = initial absolute pressure in pounds per square foot V 1 = initial volume in cubic feet T 1 = initial absolute temperature in degrees R P 2 = absolute pressure in pounds per square foot, after compression V 2 = volume in cubic feet, after compression T 2 = absolute temperature in degrees R, after compression Then:
P 1 P 2 --- 0.71 T 1 T 2 --- 2.46
V 1 V 2 --- 1.41 T 2 T 1 --- 3.46
V 1 V 2 --- 0.41 P 2 P 1 --- 0.29
V 2 V 1 --- V 2 V 1 ---
P 2 P 1 --- P 2 P 1 ---
T 2 T 1 --- T 2 T 1 ---
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These formulas are also applicable if all pressures are in pounds per square inch; if all volumes are in cubic inches; or if any other consistent set of units is used for pressure or volume. Example 1: A volume of 165 cubic feet of air, at a pressure of 15 pounds per square inch, is compressed adiabatically to a pressure of 80 pounds per square inch. What will be the volume at this pressure? V 2 V 1 165 50 cubic feet, approx. = = = Isothermal Expansion or Compression takes place when a gas is expanded or compressed with an addition or transmission of sufficient heat to maintain a constant temperature. Let: P 1 = initial absolute pressure in pounds per square foot V 1 = initial volume in cubic feet P 2 = absolute pressure in pounds per square foot, after compression V 2 = volume in cubic feet, after compression R = 53.3 T = temperature in degrees Rankine maintained during isothermal expansion or contraction Then: P 1 V 1 × P 2 V 2 × RT = = Example 2: The same volume of air as in Example 1 is compressed isothermally from 15 to 80 pounds per square inch. What will be the volume after compression? V 2 P 1 V 1 × P 2 --------- 15 165 × 80 ----------- 31 cubic feet = = = Work Required in Compression of Air: The total work required for compression and ex- pulsion of air, adiabatically compressed, is: Total work in foot-pounds 2.44 P 1 V 1 –1 = P 1 P 2 --- 0.71 15 80 --- 0.71
P 2 P 1 --- 0.29
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