hydrocarbons. The liquid compo-
nents are obtained by vacuum distil-
lation and used in lubricating oils.
The solid components (parafÜn wax)
are obtained by solvent extraction.
TheÜnal residue is a black tar con-
taining free carbon (asphaltor bitu-
men).
petroleum ether A colourless
volatileÛammable mixture of hydro-
carbons (not an ether), mainly pen-
tane and hexane. It boils in the range
30–70°C and is used as a solvent.
petroleum jelly (petrolatum) A
semi-solid mixture of hydrocarbons
extracted from petroleum. It is used
in skincare products and cosmetics,
and as a lubricant. Petroleum is
widely available under the trade-
name Vaseline.
pewterAn alloy of lead and tin. It
usually contains 63% tin; pewter
tankards and food containers should
have less than 35% of lead so that the
lead remains in solid solution with
the tin in the presence of weak acids
in the food and drink. Copper is
sometimes added to increase ductil-
ity and antimony is added if a hard
alloy is required.
peyoteSee mescaline.
Pfund seriesSee hydrogen spec-
trum.
PGA See phosphoglyceric acid.
pHSee ph scale.
phane See cyclophane.
phaseA homogeneous part of a
heterogeneous system that is sepa-
rated from other parts by a distin-
guishable boundary. A mixture of ice
and water is a two-phase system. A
solution of salt in water is a single-
phase system.
phase diagram A graph showing
the relationship between solid, liq-
uid, and gaseous *phases over a
range of conditions (e.g. temperature
and pressure). See steel (illustra-
tion).phase ruleFor any system at equi-
librium, the relationship P + F = C + 2
holds, where P is the number of dis-
tinct phases, C the number of compo-
nents, and F the number of degrees
of freedom of the system. The rela-
tionship derived by Josiah Willard
*Gibbs in 1876, is often called the
Gibbs phase rule.phase spaceFor a system with n
degrees of freedom, the 2n-dimen-
sional space with coordinates (q 1 , q 2 ,
..., qn, p 1 , p 2 , ..., pn), where the qs de-
scribe the degrees of freedom of the
system and the ps are the corre-
sponding momenta. Each point rep-
resents a state of the system. In a gas
of N point particles, each particle has
three positional coordinates and
three corresponding momentum co-
ordinates, so that the phase space
has 6N-dimensions. If the particles
have internal degrees of freedom,
such as the vibrations and rotations
of molecules, then these must be in-
cluded in the phase space, which is
consequently of higher dimension
than that for point particles. As the
system changes with time the repre-
sentative points trace out a curve in
phase space known as a trajectory.
See also attractor; configuration
space; statistical mechanics.phase transitionA change in a
feature that characterizes a system.
Examples of phase transitions are
changes from solid to liquid, liquid to
gas, and the reverse changes. Other
examples of phase transitions in-
clude the transition from a paramag-
net to a ferromagnet (see magnetism)
and the transition from a normally
conducting metal to a superconduc-
tor. Phase transitions can occur by al-407 phase transition
p