The Relation between Pressure and Volume

General Properties of Gases:
It was long known that as the pressure of a gas increases, that is, as it becomes compressed, its volume decreases, but Robert Boyle was the first to determine the exact relation between the volume and the pressure of a gas. He did this in a very simple manner.

Pour mercury into a U-shaped tube until the level of the mercury in the closed end of the tube is the same as the level in the open end. The air in the long arm is pressing upon the mercury in that arm, and is tending to force it up the short arm. The air in the short closed arm is pressing down upon the mercury in that arm and tending to send it up the long arm. Since the mercury is at the same level in the two arms, the pressure in the long arm must be equal to the pressure in the short arm. But the long arm is open, and the pressure in that arm is the pressure of the atmosphere. Therefore the pressure in the short arm must be one atmosphere. Measure the distance bc between the top of the mercury and the closed end of the tube.

Pour more mercury into the open end of the tube, and as the mercury rises higher and higher in the long arm, note carefully the decrease in the volume of the air in the short arm. Pour mercury into the tube until the difference in level bd is just equal to the barometric height, approximately 32 inches. The pressure of the air in the closed end now supports the pressure of one atmosphere, and in addition, a column of mercury equal to another atmosphere. If now the air column in the closed end is measured, its volume will be only one half of its former volume. By doubling the pressure we have reduced the volume one half. Similarly, if the pressure is increased threefold, the volume will be reduced to one third of the original volume.

FIGS. 54, 55. - As the pressure on the gas increases, its volume decreases.