The laws describing the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions are called Gas Laws. The basic gas laws were discovered by the end of the 18th century when scientists found out that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases. These macroscopic gas laws were found to be consistent with atomic and kinetic theory.
In 1643, the Italian physicist and mathematician, Evangelista Torricelli, who for a few months had acted as Galileo's secretary, conducted a celebrated experiment in Florence.[1] He demonstrated that a column of mercury in an inverted tube can be supported by the pressure of air outside of the tube, with the creation of a small section of vacuum above the mercury.[2] This experiment essentially paved the way towards the invention of the barometer, as well as drawing the attention of Robert Boyle, then a "skeptical" scientist working in England. Boyle was inspired by Torricelli's experiment to investigate how the elasticity of air responds to varying pressure, and he did this through a series of experiments with a setup reminiscent of that used by Torricelli.[3] Boyle published his results in 1662.
Later on, in 1676, the French physicist Edme Mariotte, independently arrived at the same conclusions of Boyle, while also noting some dependency of air volume on temperature.[4] However it took another century and a half for the development of thermometry and recognition of the absolute zero temperature scale, which eventually allowed the discovery of temperature-dependent gas laws.
See main article: Boyle's law. In 1662, Robert Boyle systematically studied the relationship between the volume and pressure of a fixed amount of gas at a constant temperature. He observed that the volume of a given mass of a gas is inversely proportional to its pressure at a constant temperature.Boyle's law, published in 1662, states that, at a constant temperature, the product of the pressure and volume of a given mass of an ideal gas in a closed system is always constant. It can be verified experimentally using a pressure gauge and a variable volume container. It can also be derived from the kinetic theory of gases: if a container, with a fixed number of molecules inside, is reduced in volume, more molecules will strike a given area of the sides of the container per unit time, causing a greater pressure.
Boyle's law states that:
The concept can be represented with these formulae:
V\propto
| 1 | |
| P |
P\propto
| 1 | |
| V |
PV=k1
See main article: Charles's law. Charles' law, or the law of volumes, was founded in 1787 by Jacques Charles. It states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature, assuming in a closed system.The statement of Charles' law is as follows:the volume (V) of a given mass of a gas, at constant pressure (P), is directly proportional to its temperature (T).
Charles' law states that:Therefore,
V\proptoT
{V\overT}=k2
,
where "V" is the volume of a gas, "T" is the absolute temperature and k2 is a proportionality constant (which is not the same as the proportionality constants in the other equations in this article).
See main article: Gay-Lussac's law. Gay-Lussac's law, Amontons' law or the pressure law was founded by Joseph Louis Gay-Lussac in 1808.
Gay-Lussac's law states that:Therefore,
P\proptoT
{P\overT}=k
,
where P is the pressure, T is the absolute temperature, and k is another proportionality constant.
See main article: Avogadro's law.
Avogadro's law, Avogadro's hypothesis, Avogadro's principle or Avogadro-Ampère's hypothesis is an experimental gas law which was hypothesized by Amedeo Avogadro in 1811. It related the volume of a gas to the amount of substance of gas present.[5]
Avogadro's law states that:This statement gives rise to the molar volume of a gas, which at STP (273.15 K, 1 atm) is about 22.4 L. The relation is given by:
V\propton
See main article: articles and Ideal gas law. The Combined gas law or General Gas Equation is obtained by combining Boyle's Law, Charles's law, and Gay-Lussac's Law. It shows the relationship between the pressure, volume, and temperature for a fixed mass of gas:
PV=k5T
This can also be written as:
| P1V1 | |
| T1 |
=
| P2V2 | |
| T2 |
With the addition of Avogadro's law, the combined gas law develops into the ideal gas law:
PV=nRT
where P is the pressure, V is volume, n is the number of moles, R is the universal gas constant and T is the absolute temperature.
The proportionality constant, now named R, is the universal gas constant with a value of 8.3144598 (kPa∙L)/(mol∙K).An equivalent formulation of this law is:
where P is the pressure, V is the volume, N is the number of gas molecules, kB is the Boltzmann constant (1.381×10−23J·K−1 in SI units) and T is the absolute temperature.
These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature.
This law has the following important consequences:
Prm{total}=P1+P2+P3+ … +Pn\equiv
| n | |
| \sum | |
| i=1 |
Pi,
and all component gases and the mixture are at the same temperature and volume
where Ptotal is the total pressure of the gas mixture
Pi is the partial pressure or pressure of the component gas at the given volume and temperature.
Vrm{total}=V1+V2+V3+ … +Vn\equiv
| n | |
| \sum | |
| i=1 |
Vi,
and all component gases and the mixture are at the same temperature and pressure
where Vtotal is the total volume of the gas mixture or the volume of the container,
Vi is the partial volume, or volume of the component gas at the given pressure and temperature.
p=k\rmc