3. The Dulong–Petit law, a thermodynamic rule
proposed in 1819by French physicists Pierre Louis
Dulong and Alexis Therese Petit, states the classical
expression for the molar specific heat capacity of
certain chemical elements. Experimentally the two
scientists had found that the heat capacity per weight
(the mass-specific heat capacity) for a number of
elements was close to a constant value, after it had
been multiplied by a number representing the
presumed relative atomic weight of the element.These
atomic weights had shortly before been suggested by
Dalton
4. In modern terms, Dulong and Petit found that the
heat capacity of a mole of many solid elements is
about 3R,where Ris the modern constant called the
universal gas constant. Dulong and Petit wereunaware
of the relationship with R,since this constant had not
yet been defined from the later kinetic theory of gases.
The value of 3Ris about 25joules per kelvin, and
Dulong and Petit essentially found that this was the
heat capacity of certain solid elements, per mole of
atoms they contained
5. The modern theory of the heat capacity of solids states
that it is due to lattice vibrations in the solid, and was
first derived in crude form from this assumption by
Albert Einstein, in 1907.The Einstein solid model thus
gave for the first time a reason why the Dulong–Petit
law should be stated in terms of the classical heat
capacities for gases
6. An equivalent statement of the Dulong–Petit law in
modern terms is that, regardless of the nature of the
substance, the specific heat capacity cof a solid
element (measured in joule per kelvin per kilogram) is
equal to 3R/M, where Ris the gas constant (measured
in joule per kelvin per mole) and M is the molar mass
(measured in kilogram per mole). Thus, the heat
capacity per mole of many elements is3R.
7. The initial form of the Dulong–Petit law was:
cM = K
where c is the specific heat, M the atomic weights accepted in that day,and
K is a new constant which we know today is about 3R.
In modern terms the mass m divided by atomic weight M gives the number
of moles N.
m/M = N
Therefore, using uppercase C for the total heat capacity, and lowercase c
for the specific heat capacity c :
(C/m)M = K
C(M/m) = C/N = K = 3R
or
. C/N = 3R
Therefore the heat capacity of most solid crystalline substances is 3R per
mole of substance
8.
9. Despite its simplicity, Dulong–Petit law offers fairly
good prediction for the specific heat capacity ofmany
elementary solids with relatively simple crystal
structure at high temperatures.
The Dulong–Petit law fails at room temperatures for
light atoms bonded strongly to each other, such as in
metallic beryllium, and in carbon asdiamond.
In the very low (cryogenic) temperature region, where
the quantum mechanical nature of energy storage in
all solids manifests itself with larger and larger effect,
the law fails for all substances.
