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Boyles Law

If we grant, in accordance with modern views, that matter consists of minute particles, termed molecules, it must also be allowed that the distance between these ultimate particles must be very different, according to whether the matter is in the solid, or liquid, or in the gaseous state. Thus, a cubic centimeter of water at 100 expands, when it is boiled into steam of the same temperature, to 1700 cubic centimeters; and a cubic centimeter of oxygen, measured at its boiling-point, -182, boils into 266 cubic centimeters of oxygen gas of the same temperature. In changing its state, therefore, from liquid or solid to gas, matter under goes a great alteration of volume. It is accordingly to be expected that the molecules of a gas, being at so much greater a distance from each other than the molecules of a solid or liquid, should yield more readily to pressure, and should decrease in volume when the pressure is raised, much more than solids or liquids. It is also found, as appeared probable, that the expansion of a gas is much greater than that of a solid or a liquid, by a definite rise of temperature.

Boyle's Law

The law relating to the compressibility of gases was discovered by Boyle. It is, that if temperature be kept constant, the volume of all gases is inversely as the pressure. Thus, if the pressure of the atmosphere, which is equal to 1033 grams on each square centimeter of the earth's surface at sea-level, or approximately i 5 Ibs. On each square inch, be doubled, the volume of a given weight of air, or of any other gas, will be halved ; on trebling the pressure the volume is reduced to one-third, and so on. As the length of a column of mercury, one square centimeter in cross-section, must be 76 centimeters in order that its weight shall be 1033 grams, 76 centimeters is taken as the " normal " height of the barometer. And if the height of the mercury in a gauge or "manometer" is 152 centimeters, the pressure which produces that rise in the mercurial column will halve the volume of a gas exposed to it.

Equation

The mathematical equation for Boyle's law is:

$\qquad\qquad PV = k$

where:

P denotes the pressure of the system.
V is the volume of the gas.
k is a constant value representative of the pressure and volume of the system.

So long as temperature remains constant at the same value the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of k will remain constant. However, due to the derivation of pressure as perpendicular applied force and the probabilistic likelihood of collisions with other particles through collision theory, the application of force to a surface may not be infinitely constant for such values of k, but will have a limit when differentiating such values over a given time.

Forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure p must decrease proportionally. Conversely, reducing the volume of the gas increases the pressure.

Boyle's law is used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas. The before and after volumes and pressures of the fixed amount of gas, where the before and after temperatures are the same (heating or cooling will be required to meet this condition), are related by the equation:

$p_1 V_1 = p_2 V_2. \,$

Boyle's law, Charles's law, and Gay-Lussac's law form the combined gas law. The three gas laws in combination with Avogadro's law can be generalized by the ideal gas law.

Boyles Law

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