# Boyle Point

## Boyle Point

the minimum point on an isotherm of a real gas, represented in (p, pV) coordinates. (See Figure 1; ρ is the pressure of the gas and V is the volume occupied by the gas.) It is named for the English scientist R. Boyle.

Figure 1. Isotherms of a real gas [in (p, pV) coordinates] that characterize the compressibility of the gas. T0, is the Boyle temperature; Boyle points are absent on isotherms with temperature T > TB.

In the vicinity of the Boyle point, small sections of the isotherm of a real gas can be considered approximately as segments of horizontal straight lines that according to the Clapeyron equation pV = mRT represent the isotherms of an ideal gas. (T is the absolute temperature, R is the gas constant, and m is the mass of the gas.) In other words, the Boyle point determines the temperature at which, for a given real gas, the equation of an ideal gas is applicable. The section of the isotherm ab (to the left of the Boyle point) corresponds to the conditions under which a real gas is more compressible than an ideal gas; the section bc (to the right of the Boyle point) corresponds to the conditions of lower compressibility of a real gas in comparison with an ideal gas. The dominant influence of the forces of attraction between molecules, which facilitates the contraction of a gas, becomes apparent to the left of the Boyle point; the influence of the volume of the molecules themselves, which hinders contraction, appears to the right of the Boyle point. In the vicinity of the Boyle point, these factors—which distinguish a real gas from an ideal gas—compensate each other.

The line that connects the Boyle points of individual isotherms is called the Boyle curve. The point of this curve that lies on the y-axis (p = 0) determines the so-called Boyle temperature (TB). For a gas that obeys the van der Waals equation, TB = 3.375 Tc, where Tc is the critical temperature. For T < Tc the complete liquefaction of the gas under pressure is possible; for T < TB, partial liquefaction of gases is possible upon throttling.

IU. N. DROZHZHIN

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