change from A to B, and VBand VA
are the volumes of B and A respec-
tively. In the case of a transition from
liquid to vapour, the volume of the
liquid can be ignored. Taking the
vapour to be an *ideal gas, the
Clapeyron–Clausius equation can be
written:
dlogep/dT = L/RT^2
The Clapeyron–Clausius equation is
named after the French engineer
Benoit-Pierre-Émile Clapeyron
(1799–1864) and Rudolf *Clausius.Clark cellA type of *voltaic cell
consisting of an anode made of zinc
amalgam and a cathode of mercury
both immersed in a saturated solu-
tion of zinc sulphate. The Clark cell
was formerly used as a standard of
e.m.f.; the e.m.f. at 15°C is 1.4345
volts. It is named after the British sci-
entist Hosiah Clark (d. 1898).Clark process See hardness of
water.clathrateA solid mixture in which
small molecules of one compound or
element are trapped in holes in the
crystal lattice of another substance.
Clathrates are sometimes called
enclosure compounds or cage com-
pounds, but they are not true com-
pounds (the molecules are not held
by chemical bonds). Quinol and ice
both form clathrates with such sub-
stances as sulphur dioxide and xenon.Claude process A process for liq-
uefying air on a commercial basis.
Air under pressure is used as the
working substance in a piston en-
gine, where it does external work
and cools adiabatically. This cool air
is fed to a counter-current heat ex-
changer, where it reduces the tem-
perature of the next intake of
high-pressure air. The same air is re-
compressed and used again, and after
several cycles eventually liqueÜes.The process was perfected in 1902 by
the French scientist Georges Claude
(1870–1960).
claudetiteA mineral form of *ar-
senic(III) oxide, As 4 O 6.Clausius, Rudolf Julius Em-
manuel(1822–88) German physi-
cist, who held teaching posts in
Berlin and Zurich, before going to
Würzburg in 1869. He is best known
for formulating the second law of
*thermodynamics in 1850, indepen-
dently of William Thomson (Lord
*Kelvin). In 1865 he introduced the
concept of *entropy, and later con-
tributed to electrochemistry and elec-
trodynamics (see clausius–mossotti
equation).Clausius inequalityAn inequality
that relates the change in entropy dS
in an irreversible process to the heat
supplied to the system dQ and the
thermodynamic temperature T, i.e.
dS ≥dQ/T. In the case of an irre-
versible adiabatic change, where dQ =
0, the Clausius inequality has the
form dS >0, which means that for
this type of change the entropy of
the system must increase. The in-
equality is named after Rudolf Julius
Emmanuel *Clausius. The Clausius
inequality can be used to demon-
strate that entropy increases in such
processes as the free expansion of a
gas and the cooling of an initially hot
substance.Clausius–Mossotti equationA
relation between the *polarizability
αof a molecule and the dielectric
constant εof a dielectric substance
made up of molecules with this po-
larizability. The Clausius–Mossotti
equation can be written in the form
α= (3/4πN)/[(ε– 1)/(ε– 2)],
where N is the number of molecules
per unit volume. The equation pro-
vides a link between a microscopicClark cell 128c