Law of Mariotte

The law of Mariotte is one of the laws of the Thermodynamique of the real Gaz. It Connects the pressure and the volume of a real Gaz to constant temperature. One thus plots an isothermal curve of gas. Mariotte and Boyle noted, with a margin of a few percent, that the curve p = F (V) was close to a hyperbole équilatère in coordinates known as of Clapeyron (p, V), that is to say statement = cste at a constant given temperature.

In other words, to maintain the temperature constant during an increase in pressure of a gas requires a reduction in volume. Conversely, the reduction of the pressure of gas passes by an increase in volume. The exact value of the constant does not need to be known to apply the law between two volumes of gas under different pressures, at the same temperature:

p_1 \ times V_1 = p_2 \ times V_2

The law was discovered at a few years of interval by the Irishman Robert Boyle (in 1662) and by the French Edme Mariotte (in 1676). Therefore, some name it law of Boyle , and more “diplomatic” call it law of Boyle-Mariotte . It is Guillaume Amontons which specified in 1702 which this law is valid only at constant temperature and is more precise with the low pressures.

universal Law of Avogadro

If the pressure is low, product statement is the same one, at a given temperature, whatever the pure substance considered: it is the law of Avogadro (1811) (cf Nombre of Avogadro $N_A$ ). As this quantity is a linear function of the temperature. One falls down on the equation of state of the Perfect gas: statement = nRT

Let us determine the value of R, the constant of perfect gas:

If one considers 1 mole of perfect gas under the normal conditions of temperature and pressure: R = p₀V₀/T₀

p₀ = 1 atm = 1,01325 bar (1 bar = 10⁵ Pa),
T₀ = 273,15K,
V₀ (molar volume) = 22,414.10^-3 m³.

One finds R = to 8,314 J.K^-1.mol^-1.

Applications

The phenomenon stated by the law of Mariotte has very important consequences for the plungers. At the time of a Plunged underwater, one breathes of the compressed air. But, in water, the pressure increases by a bar every approximately ten meters. Consequently, at the time of the increase, the air which was compressed will slacken and thus increase its volume. Consequently, if one blocks his breathing during the increase, the air contained in the lungs which cannot escape, it will distend them and cause the rupture of fabrics. That is called the pulmonary overpressure. It is thus important to make it possible the air to escape at the time of the increase by not blocking its breathing.

In the same way, the gases dissolved under the effect of the higher pressure (it is especially the case for the Azote) in blood and the body fabrics go at the time gone up to turn over at the gas state, causing an increase in volume. It is thus necessary to respect stages of decompression, in order to allow an evacuation controlled by expiry, in a progressive and nonbrutal way, gases and to thus avoid a gas embolism. But in a strict sense, this is not an application of the Law of Mariotte, since part of the phenomenon is related to the variation of solubility of gases in a liquid according to the exerted pressure.

Random links: