Isothermal expansion and compression may be clearly illustrated by means of a diagram like that shown in Fig. 13. Suppose that 10 cubic feet of air at a pressure of 10 pounds, absolute, is compressed isothermally until its volume is only 2 cubic feet. On the diagram, the lines OP and OV are drawn at right angles to each other, and equal distances or divisions are laid off on each line. The line OP is called the
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axis of pressures, and OV is called the axis of volumes. Each division laid off vertically, or in the direction of OP represents a pressure of 5 pounds; and each horizontal division, in the direction of OV, represents 1 cubic foot. Hence, the state of a gas having a volume of 10 cubic feet at a pressure of 10 pounds must be represented by the point K, since K lies vertically above 10 on the axis of volumes and on the horizontal line through 10 on the axis of pressures.
74. The product of the pressure and volume at the point K is 10 × 10 = 100. Now, since the air is to be compressed isothermally, the product of the pressure and volume at any other state must be 100. Suppose that the air is compressed until its volume is only 9 cubic feet. Its pressure in that state must then be 100 ÷ 9 = 1119 pounds. The point H, vertically above 9 and opposite 1119 on the pressure scale, then represents that state of the gas. When the volume is compressed to 8 cubic feet, the pressure is 100 ÷ 8
