CHAP. 2: STATE BEHAVIOUR [CONTENTS] 48
2.2 Equations of state.
2.2.1 Concept of the equation of state.
The term equation of state is used for the relation between temperature, pressure, volume and
amount of substance in an analytic form, i.e.
f(p, V, T, n) = 0. (2.12)Given that volume is an extensive quantity (see1.3.1), we can write the equation of state as
a relation between three variables
φ(p, Vm, T) = 0. (2.13)
Equations of state are usually written in the form
p=f(T, Vm) or z=f(T, Vm) or z=f(T, p). (2.14)2.2.2 Equation of state of an ideal gas
p=nRT /V or p=RT /Vm or z= 1. (2.15)Note:If we use other than base units forp,V,T,n, then the gas constantRmay have a
value other than 8.314 J mol−^1 K−^1.
The following laws, historically preceding the equation of state of an ideal gas, led to relation
(2.15).
- Boyle’s law—at constant temperature and constant amount of substance we have
pV = const, [T, n]. (2.16)- Gay-Lussac’s law—at constant pressure and constant amount of substance, the volume
of a system is proportional to its absolute temperature
V = constT , [p, n]. (2.17)- Avogadro’s law—molar volumes of different gases at the same temperature and pres-
sure have the same values.