PHYSICAL CHEMISTRY IN BRIEF

CHAP. 2: STATE BEHAVIOUR [CONTENTS] 49

Vm= const, [p, T]. (2.18)

S Symbols:The symbol [X, Y,.. .] denotes that the equation applies at constantX, Y,...

2.2.3 Virial expansion.

The virial expansion is an equation of state in which the compressibility factor is expressed in

the form of a power series of 1/Vm, or in the powers ofc

z = 1 +B(T)/Vm+C(T)/Vm^2 +···

= 1 +B(T)c+C(T)c^2 +···. (2.19)

QuantitiesB,C,... are calledvirial coefficients;Bis the second virial coefficient,Cis the
third virial coefficient, etc.
S Symbols: By writingB(T),C(T) we indicate that in a pure substance, the virial coefficients
are functions of temperature only (while in a mixture they also depend on composition).

2.2.4 Boyle temperature

The temperature at which the second virial coefficient is zero,B = 0, is called the Boyle

temperature,TB. At this temperature and in its vicinity, the approximationz= 1 (the equation

of state of an ideal gas) is fulfilled with a high accuracy even at relatively high pressures. At

temperaturesT < TB,B <0; atT > TB,B >0.

Example

Calculate the Boyle temperature if the dependence of the second virial coefficient on temperature

isB=a−b/T, wherea, bare constants.

Solution

Given thatB= 0, we haveTB=b/a.