# Gas Laws

## Definition

The gas laws are mathematical formulations of the interrelationships among the four variables that describe the behavior of a gas sample: its volume (V), pressure (P), temperature (T), and the amount (n) of gas present (see Gases, properties of).

The properties of gases were already being studied and described as early as the seventeenth century. Unlike solids, which have a fixed shape and volume, and liquids, which have a fixed volume but can change shape according to the container, gases assume both the shape and the volume of their container. The volume of space occupied by a sample of gas depends on the number of gas mole-cules present and the sample's pressure and temperature.

## Boyle's law

Boyle's law, formulated by English scientist Robert Boyle in 1662, states that the pressure of a fixed amount of gas at a constant temperature is inversely proportional to its volume. In other words, when a sample of gas is allowed to expand to occupy a larger volume, its pressure decreases; and when it is compressed into a smaller volume, its pressure increases. Mathematically, this inverse relationship may be formulated:

P1V1 = P2V2

or

V = constant ÷ P

In continental Europe, this gas law is known as the law of Mariotte, after Edme Mariotte, who published the results of his studies of the properties of gases a few years later than Boyle.

The working of a syringe can be used to illustrate Boyle's law. When the plunger of a syringe is drawn back, the volume of the air inside the syringe barrel is increased and the pressure decreased relative to the exterior of the syringe, and fluid is pulled into the syringe. When the plunger is depressed, the volume is decreased, the pressure increased, and fluid is forced out.

## Charles's law

Charles's law, which was formulated by French physicist Jacques Charles in 1787, states that the volume of a sample of gas kept at constant pressure is directly proportional to the temperature; or, more simply stated, a gas sample will expand upon heating and contract when cooled. This may be formulated mathematically as:

V1 ÷ T1 = V2 ÷ T2

or

V = constant× T

A hot air balloon demonstrates the principle of Charles's law. When the balloon is fired, the air is heated and expands to fill the balloon.