Matura diamondSee zircon.
Maxwell, James Clerk (1831–79)
British physicist, born in Edinburgh,
who held academic posts at Ab-
erdeen, London, and Cambridge. In
the 1860s he was one of the founders
of the *kinetic theory of gases, but
his best-known work was a mathe-
matical analysis of electromagnetic
radiation, published in 1864.
Maxwell–Boltzmann distribu-
tionA law describing the distribu-
tion of speeds among the molecules
of a gas. In a system consisting of N
molecules that are independent of
each other except that they exchange
energy on collision, it is clearly im-
possible to say what velocity any par-
ticular molecule will have. However,
statistical statements regarding cer-
tain functions of the molecules were
worked out by James Clerk Max-
well and Ludwig Boltzmann. One
form of their law states that
n = Nexp(–E/RT), where n is the num-
ber of molecules with energy in ex-
cess of E, T is the thermodynamic
temperature, and R is the *gas con-
stant.
Maxwell’s demon An imaginary
creature that is able to open and shut
a partition dividing two volumes of a
gas in a container, when the two vol-
umes are initially at the same tem-
perature. The partition operated by
the demon is only opened to allow
fast molecules through. Such a
process would make the volume of
gas containing the fast molecules
hotter than it was at the start; the
volume of gas remaining would ac-
cordingly become cooler. This
process would be a violation of the
second law of thermodynamics and
therefore cannot occur. Maxwell’s
demon was invented by James Clerk
Maxwell in a letter written in 1867 to
show that the second law of thermo-
dynamics has its origins in statisti-
cal mechanics, although the name
was suggested by the Scottish scien-
tist Sir William Thomson
(1824–1907; subsequently Lord
Kelvin).
Maxwell’s thermodynamic
equationsEquations in thermody-
namics for a given mass of a homo-
geneous system, relating the entropy
(S), pressure (p), volume (V), and ther-
modynamic temperature (T). The
four equations are:
(∂T/∂V)s= –(∂p/∂S)V;
∂T/∂p)s= –(∂V/∂S)p;
(∂V/∂T)p= –(∂S/∂p)T;
(∂S/∂V)T= –(∂p/∂T)V.
Mayerf-functionA quantity that
occurs in the calculation of virial
coefÜcients; it is deÜned by f =
exp(–V 2 /kT) – 1, where V 2 is the two-
body interaction potential energy, k
is the *Boltzmann constant, and T is
the thermodynamic temperature. It
is related to the second virial coefÜ-
cient B by:
B = (–NA/V)∫fdr 1 dr 2 ,
where NAis the Avogadro number
and V is the volume of the system.
This equation simpliÜed to:
B = –2πNA∫∞
0 fr^2 dr
in the case of closed-shell atoms and
octahedral and tetrahedral mol-
ecules. When particles are so far
apart that the interaction V →0,
then f →0 also, but when the parti-
cles are so close together that the in-
teraction V →∞, then f →–1. This
enables strong repulsive interactions
between particles to be analysed in
terms of f but not of V. The function
is named after the US physicist
Joseph Mayer.Mayer’s test A general *presump-
tive test for cocaine, morphine,
heroin, and other alkaloids. Mayer’s
reagent is a solution of potassium
mercury iodide in water. A positive345 Mayer’s test
m