A-to-Z Guide to Thermodynamics,
Heat & Mass Transfer, and Fluids Engineering

One of the main (along with Charles', Boyle-Mariotte's and Avogadro's laws) empirical laws of ideal gases was established by J. Gay-Lussac in 1802. According to the Gay-Lussac Law, at constant (and low) pressure P the volume of the given gas mass M varies linearly with temperature: Vt = V0 + AΔT, where Vt and V0 are gas volumes at temperatures T and T0, ΔT = T – T0, A = V0αp = const, αp = V−1 (∂V/∂t)p is the isobaric volume expansion coefficient, i.e., VT = V0 + V0αpΔT = V0(1 + αpΔT). The quantity αp for gas is found to be independent of gas nature and pressure, but dependent on temperature; in this case at T0 = 0°C, αp = 273.15–1°C–1. The Gay-Lussac Law (GLL) describes the isobaric process of an ideal gas.

The GLL has played principal part in establishing the notion of absolute temperature and in deriving the universal equation of ideal gas state—the Clapeyron (Clapeyron-Mendeleyev) equation. At T0 = 0°C and T = –273.15°C the ideal gas volume Vt = 0, i.e., the linear isobar of ideal gas vanishes at this temperature, thus intersecting the temperature axis. When temperature is counted from this thermodynamically minimally possible level, the GLL provides already not merely linear, but proportional dependence of gas volume on this absolute temperature T. The comparison, in this case, of the GLL with the other empirical ideal-gas laws (Charles', Boyle-Mariotte's and Avogadro's laws) allows a general equation of state of ideal gases , where is the molecular mass of gas, R is the universal gas constant (R = 8.314 J/mole K).

Like the other ideal-gas laws, including the Clapeyron-Mendeleyev law, the GLL, which is a particular case of the latter one, is valid at low pressures (far from critical one), when the influence of the actual size of particles and their forces of interaction is absent. The GLL that was established by empirical method and the notions obtained on its basis have been subsequently substantiated by using the molecular-kinetic theory. In particular, the physical meaning of absolute temperature T consists in the fact, that this quantity is proportional to the mean kinetic energy of translational motion of particles.

Of great importance in developing the universal equation of state of ideal gases and, in particular, in discovering Avogadro's law, according to which under equal conditions (p and T values) the number of moles in a unit volume of any gas is the same (or 1 mole occupies the same volume that is equal at normal pressure p = 0.1013 MPa and t = 0°C to the value of 22.4 liters) was the law established by Gay-Lussac in 1808. This law states that the volumes of gases entering a chemical reaction relate to each other and to the volumes of gas products of a reaction as the ratios of small integers (for example, for the 2H2 + O3 = 2H2O reaction this relation is 2:1:2).

Similarly to the GLL for volumes, the linearity of pressure of the given mass M of ideal gas at constant volume V establishes Charles law (1787), namely, pT = p0(1 + αvT), where pT and p0 are gas pressures at temperatures T and T0, and the parameter αv is the isochoric coefficient of pressure αv = p−1(∂p/∂T)v = f(T), where for ideal gas αp = αv and, accordingly, at T = 273.15°C αv = 271.15−1°C−1. Charles law describes the isochoric process of ideal gas.