The relationship between volume and pressure of a given amount of gas at constant temperature was first published more than 300 years ago by the English natural philosopher Robert Boyle. It is summarized in the statement now known as Boyle`s law: the volume of a given amount of gas maintained at a constant temperature is inversely proportional to the pressure under which it is measured. The kinetic theory of gases relates the macroscopic properties of gases, such as pressure and volume, to the microscopic properties of the molecules that make up the gas, in particular the mass and velocity of the molecules. To derive Charless` law from kinetic theory, it is necessary to have a microscopic definition of temperature: it can easily be assumed that it is the temperature proportional to the average kinetic energy of gas molecules, Ek: use of P1 and V1 as known values 0.993 atm and 2.40 ml, P2 as pressure at which volume is unknown, and V2 as unknown volume, we have: During the seventeenth and especially eighteenth centuries, driven both by the desire to understand nature and by the search for balloons in which they could fly (Figure 1), a number of scientists noted the relationships between the macroscopic physical properties of gases, i.e. pressure, the volume, temperature and quantity of gas. Although their measurements were not accurate by current standards, they were able to determine the mathematical relationships between pairs of these variables (e.g., Pressure and Temperature, Pressure and Volume) that apply to an ideal gas – a hypothetical construct that real gases approximate under certain conditions. Eventually, these individual laws were combined into a single equation – the ideal gas law – which relates gas quantities for gases and is accurate enough for low pressures and moderate temperatures. We will examine the most important developments in each relationship (not quite in historical order for pedagogical reasons) and then summarize them in the ideal gas law. However, I can note that if the temperature of ether is only slightly above its boiling point, its condensation is slightly faster than that of atmospheric air.

This fact is related to a phenomenon that many bodies present during the transition from the liquid state to the solid state, but which is no longer perceptible at temperatures a few degrees above that at which the transition takes place. [3] [latex]dfrac{{V}_{1}}{{T}_{1}}=dfrac{{V}_{2}}{{T}_{2}}text{, which means that }dfrac{0.300text{ L}}{283text{ K}}=dfrac{{V}_{2}}{303text{ K}}[/latex] Since we are looking for the change in volume caused by a change in temperature at constant pressure, this is a task for Charlemagne Law. Taking V1 and T1 as initial values, T2 as temperature at which volume is unknown, and V2 as unknown volume, and converting °C to K, we obtain: but I can mention that the latter conclusion can only be true as long as the compressed vapours remain completely elastic; This requires that their temperature be high enough that they can withstand the pressure that causes them to assume the liquid state. [3] The first mention of a temperature at which the volume of a gas could fall to zero was made by William Thomson (later known as Lord Kelvin) in 1848:[7] However, the “absolute zero” on the Kelvin temperature scale was originally defined by the second law of thermodynamics, which Thomson himself described in 1852. Thomson did not assume that this was equal to the “zero volume point” of Karl`s law, but only that Charles` law predicted the minimum temperature that could be reached. The two can be shown as equivalent by Ludwig Boltzmann`s (1870) statistical view of entropy. Absolute zero: The temperature at which the volume of a gas would be zero according to Charlemagne`s law. (Note: Note that this particular example is an example where the assumption of ideal gas behavior is not very reasonable because it is gas with relatively high pressures and low temperatures.

Despite this limitation, the calculated volume can be considered a good rough estimate.) This is what can be expected if we consider that infinite cold must correspond to a finite number of degrees of air thermometer below zero; because if we take far enough the strict principle of graduation mentioned above, we should arrive at a point corresponding to the reduction of the air volume to zero, which would be marked as −273° of the scale (−100/.366 if .366 is the coefficient of expansion); And that is why −273° of the air thermometer is a point that cannot be reached at any finite temperature, no matter how low. The Italian scientist Amedeo Avogadro hypothesized in 1811 to explain the behavior of gases, explaining that equal volumes of all gases, measured under the same conditions of temperature and pressure, contain the same number of molecules. Over time, this relationship has been supported by numerous experimental observations, as expressed by Avogadro`s law: for a trapped gas, the volume (V) and the number of moles (n) are directly proportional if the pressure and temperature remain constant. Boyle`s Law: The volume of a given number of moles of gas maintained at a constant temperature is inversely proportional to the pressure under which it is measured Figure 3. For a constant volume and volume of air, pressure and temperature are directly proportional if the temperature is expressed in Kelvin. (At lower temperatures, measurements cannot be made due to gas condensation.) When extrapolated to lower pressures, this line reaches a pressure of 0 to -273 °C, which is 0 on the Kelvin scale and the lowest possible temperature, called absolute zero. For a limited and constant volume of gas, the ratio [latex]dfrac{P}{T}[/latex] is therefore constant (i.e. [latex]dfrac{P}{T}=k[/latex] ). If the gas is first in “state 1” (with [latex]P = P_{1}text{ and }T = T_{1})[/latex], then switches to “condition 2” (with [latex]P=P_{2}text{ and }T = T_{2})[/latex], we have [latex]dfrac{{P}_{1}}{{T}_{1}}=k[/latex] and [latex]dfrac{{P}_{2}}{{T}_{2}}=k,[/latex], which is reduced to [latex]dfrac{{P}_{1}}{{T}_{1}}=dfrac{{P}_{2}}{{T}_{2}}[/latex]. This equation is useful for pressure-temperature calculations for a closed gas at constant volume.

Note that for all calculations of the law of gases, the temperatures must be on the Kelvin scale (0 on the Kelvin scale and the lowest possible temperature is called absolute zero). (Also note that there are at least three ways in which the pressure of a gas changes when its temperature changes: We can use an array of values, a graph, or a mathematical equation.) Dalton was the first to show that the law generally applies to all gases and vapors of volatile liquids when the temperature is well above the boiling point. Gay-Lussac agreed. [6] Using only measurements at the two fixed thermometric points of water, Gay-Lussac could not show that the equation relating volume and temperature is a linear function. For purely mathematical reasons, Gay-Lussac`s work does not allow the attribution of a law indicating the linear relation. The main conclusions of Dalton and Gay-Lussac can be expressed mathematically as follows: where V100 is the volume taken by a given gas sample at 100 °C; V0 is the volume occupied by the same gas sample at 0 °C; and k is a constant that is the same for all gases at constant pressure. This equation does not include temperature and is therefore not what has become known as Charlemagne`s law. The Gay-Lussac value for k (1⁄2.6666) was identical to the earlier Dalton value for vapours and remarkably close to the current value of 1⁄2.7315. Gay-Lussac attributes this equation to unpublished statements by his Republican colleague J. Charles in 1787. In the absence of a clear record, the law of gases concerning volume and temperature cannot be attributed to Charles.

Dalton`s measurements had a much larger temperature range than Gay-Lussac`s, measuring not only volume at solid points in water, but also at two points in between. Ignoring the inaccuracies of the mercury thermometers of the time, which were divided into equal parts between the fixed points, Dalton, having concluded in Test II that in the case of vapours “every elastic liquid expands almost uniformly into 1370 or 1380 parts of heat of 180 degrees (Fahrenheit), could not confirm this for gases. Calculate the bar pressure of 2520 moles of hydrogen gas stored at 27 °C in the 180 L storage of a modern hydrogen-powered car. Rearrangement of the equation to be solved for the final volume: Avogadro law: The volume of a gas at constant temperature and pressure is proportional to the number of gas molecules Gases whose properties of P, V and T are precisely described by the law of perfect gases (or other laws of gases) are intended to exhibit ideal behavior or to approximate the properties of an ideal gas. An ideal gas is a hypothetical construct that can be used with kinetic molecular theory to effectively explain the laws of gas, as described in a later module of this chapter. Although all calculations presented in this module assume ideal behavior, this assumption only makes sense for gases under relatively low pressure and high temperature. In the last module of this chapter, an amended gas law is introduced, which takes into account the less-than-ideal behaviour of many gases at relatively high pressures and temperatures. Charlemagne`s law is a special case of the ideal gas law. It indicates that the volume of a solid mass of a gas is directly proportional to temperature. This law applies to ideal gases that are maintained at a constant pressure, only the volume and temperature can change.