was taken away from the gas (cooled) in order that work might be done. In both cases, the amount of work done was proportional to the amount of heat supplied or taken away, and, had the work done been the same, the amount of heat supplied or taken away would also have been the same.
69. When a body free to expand is heated, two operations are performed: first, the temperature is raised and its volume is increased; secondly, the body, in expanding, overcomes the outer pressure, and thus does work. Suppose that 1 cubic foot of air is confined in a cylinder having a sectional area of 1 square foot. The height of the column of air in the vessel is then 1 foot. Let the original temperature of the air be 70° F., and let it be heated until the temperature is 100° higher, or 170° F. The new volume is determined by formula 2, Art. 40, to be
cubic feet, nearly.
The increase, in volume, is 1.19 — 1 = .19 cubic foot; and, since the area of the cylinder becomes no greater, the column of air must become .19 foot longer. Hence, the piston will be raised a distance of .19 foot. In expanding, the pressure of the atmosphere (equaling a weight of 144 X 14.7 = 2,116.8 pounds, since the area of the cylinder is 144 square inches) was overcome through a distance of .19 foot, and work was done equivalent to 2,116.8 × .19 = 402.19 foot-pounds. The greater part of the heat went to increase the temperature, and this action is called the Inner, or Internal, work. The work of overcoming the outside pressure through a certain distance, by expanding, is called the outer, or external, work.
70. The weight of a cubic foot of air having a temperature of 70° is found by means of formula 5, Art. 38, . Dividing both sides of this equation by ,
or
Substituting the values of , , , and ,
pound nearly
