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Heat Treatment REPORTS
Specific heat capacity of alu-
minium and aluminium alloys
by Dan Dragulin, Marcus Rüther
Material and product designing in the field of aluminium and aluminium alloys is a permanent challenge. The present
paper embraces an important thermodynamical aspect, the specific heat, of a metal having an extreme large representa-
tion in the industry: aluminium. The various applications (from heat treatment to ablative materials and nuclear fuel)
analyzed within the framework of the present paper reveal the utmost representativity of the topic (Preamble by Oleg
Hoffmann – BAGR Berliner Aluminiumwerk GmbH).
S
pecific heat capacity (as intensive property) or heat
capacity (as extensive property) is a fundamental
concept of thermodynamics having a seminal impor-
tance for practical applications.
The specific heat capacity builds the very basis of every
theoretical and practical heat transfer calculation. The
present work will delineate the above mentioned practical
importance of the specific heat capacity in the case of alu-
minium using various methods of calculation. The differences
resulted from the application of different methods could
appear, at the first glance, to be not significant, but for large
industrial applications (such as heat treatment of aluminium),
lead to significant technical and economical consequences.
Principally the perception of the specific heat capacity has
not changed since 1760 (the year of the first documented
approach of “specific heat”) till today (“The heat capacity is a
constant that tells how much heat is added per unit temper-
ature rise. The value of the constant is different for different
materials.” [1]) What is changing is the accuracy of estimation.
Table 1 shows an outline of the historical development.
Table 1: Historical development [2]
Name Year Person
1760 Joseph Black (1728-1799) Scottish physicist and chemist
Absolute heat 1770s William Irvine (1743-1787) Irish chemist and physician
Specific fire c.1777 Richard Kirwan (1733-1812) Irish chemist
Capacity of bodies for receiving the matter of heat c.1777 Richard Kirwan
Absolute heat of bodies 1779 Adair Crawford (1748-1795) Irish chemist
Specific heat 1780 Joao Magellan (1722-1790) Portuguese physicist
Specific heat 1782 Johann Wilcke (1732-96) Swedish chemist
Capacities [of substances] for heat 1807 Thomas Young (1773-1829) English polymath
Caloric specific 1824 Anon, Dictionary of Chemistry
Capacity for heat / Specific heat 1846 Karl Friedrich Peschel
Heat-capacity 1848 Leopold Gmelin (1788-1853) German chemist
Specific heat | Capacity of bodies for heat 1860 John Johnston
Specific heat (capacity for heat referred to a given
weight)
1861 Leopold Gmelin
Specific heat [Capacity for heat] 1865 Rudolf Clausius (1822-1888) German physicist
Real specific heat [Real capacity for heat] 1865 Rudolf Clausius
Specific heat capacity 1869 Anon, Nature, Vol. 290
Specific heat-capacity 1880
James Hamblin Smith, An Introduction to the Study of
Heat
Heat capacity 1894 Wilhelm Ostwald
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REPORTS Heat Treatment
The following calculations are based on data and methods
published after 1900.
BASIC NOTIONS
The following definitions are from Atkins [3].
Heat capacity at constant volume – extensive property:
C
T
U
V
V
J
L
K
K
K
K
K
N
P
O
O
O
O
O
where: U: internal energy; T: temperature [Kelvin].
Molar
1 heat capacity at constant volume – intensive prop-
erty:
C
n
c
V m,
V = [J K
Analogue to the heat capacity at constant volume:
Heat capacity at constant pressure – extensive property:
C
T
H
p
p
J
L
K
K
K
K
K
N
P
O
O
O
O
O
where: H: enthalpy; T: temperature.
The molar heat capacity at constant pressure C p,m is an
intensive property.
2
DATA AND CALCULATION METHODS
The variation of heat capacity with temperature can some-
times be ignored if the temperature range is small; this
approximation is highly accurate for a monoatomic perfect
gas (Atkins [3]). This statement is very often, in practice,
completely ignored: calculations performed using a single
value for a large temperature interval (the case of alumini-
um heat treatment processes) are a common practice with
negative economic consequences.
Formulae such as (4) & (5) [4] should be avoided in
the practice of heat treatment. Later in this article other
approaches will be presented:
1 C V,s =C v /m – specific heat capacity: the heat capacity of the sample
divided by the mass, usually in grams; analogue for C p,m
2 In the case of quoted material all notations, spelling and measuring units
correspond to the original
q = m · C · DT (4)
q = m · C · (T f
– T
i
q = amount of heat energy gained or lost by substance
m = mass of sample
C = heat capacity (J
o C
T
f = final temperature
T
i = initial temperature
In the case of a heat treatment process
3 the temperature
variation is the core of the process and therefore has to be
taken into account. Table 2 presents several approxima-
tion expressions delineating the dependency of the heat
capacity of the temperature; the values
4 of the equation
parameters (e. g. a, b, c …) are to be found in the respec-
tive literature source and are valid only for the specified
temperature interval. For practical applications the energy
required to heat a product can be calculated using the
formula (6).
Q m · C dt p T
T
i
f
= y (6)
Fig. 1 provides a graphic depiction of literature data show-
ing, for some temperature intervals, significant differences.
For the intervals where these differences, at the first glance,
are not significant one has to take into account the global
quantity of material submitted to an industrial heat treat-
ment process.
Fig. 2 shows results of recent research works [8]; the
inherent differences are clearly depicted.
Pure aluminium is for the practice of heat treatment
not relevant. Aluminium alloys are the object of industrial
heat treatment processes. The best way to get credible
information about their heat capacity is to measure it; a
very recent publication [11] provides valuable data con-
cerning the AlSi7Mg0.3 alloy. These data are, together with
the calculation (after [5]) for pure Al, presented in Fig. 3.
Between the two sorts of AlSi7Mg0.3 alloys there are no
significant differences, but between pure Al and the alloy
the differences are significant. Therefore, the transfer of
data from pure Al to Al-alloys has to take into account the
inherent significant differences.
In the case of alloy one can use Kopp´s law: “The molec-
ular heat capacity of a solid compound is the sum of the
atomic heat capacities of the elements composing it; the
elements having atomic heat capacities lower than those
required by the Dulong-Petit law retain these lower values
in their compounds.” [Wikipedia]
C C ·x i i i
n
1
=
/ _ i (7)
3 A heat treatment process is a heat transfer process; the present paper
refers to solid state heat transfer processes.
4 (Of course) are different from author to author
Table 2: Heat capacity for aluminium – approximate
expressions
C p
Source
C p,m = a + bT + c / (T
2 ) [3]
C p = a + bT – c / (T
2 ) [5]
C p
= a + bT +c(T²) + d(T³) + e / (T²) [6]
C p = aT + b(T³) + c / (T²) (^) [7] " [8]
C p = a(T
b )(e
cT )(e
d / T ) [8]
C p = a + bT + c / (T
2 ) [9] " [8]
(C p
0 (T)) / R = a 1
2 ) + a 4 (T
3 )+ a 5 (T
4 )
R = universal gas constant
[10]
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for space working objects. “The rate of temperature change
may also reveal information about the heat capacity of
the target or of its outer layer. For example, a light bal-
loon decoy (with a low heat capacity) would be expected
to change temperature much more rapidly than a heavy
warhead.” [17]
ALUMINIUM AS ABLATIVE MATERIAL
In the case of re-entry vehicles, the designing of the heat
shields using ablative materials has to take into account
not only the density and the melting point of the respec-
tive material, but also thermodynamic properties such
as the specific heat. Due to these mixtures of properties
aluminium is one of the most important ingredients for
ablative materials (along with other materials such as: Be,
Cu, Graphite, Fe, Mo, Ni, Ag, Au, W); for further information
see [18].
In the case of specific heat transfer ablative, multilayer
materials or coatings the relationship between heat capaci-
ty and the elasticity modulus is very important. Table 3 will
present a comparison between aluminium, silver and gold.
As these data show, the competitiveness of aluminium is
indisputable (do not forget the other strategic properties
of aluminium exposed above).
Conclusion The present paper presents various results
regarding the implication of the accuracy (without making
a mathematical excursus trying to define the difference
between accuracy vs. precision) of a large variety of meth-
ods and algorithms to calculate or to estimate the value of
the specific heat capacity. The choice of the estimation/
calculation method has to take into account the very spe-
cific temperature interval and the very specific material.
In the case of industrial heat treatment/transfer processes
of Al-alloys, the production specialist has very little data at
Fig. 4: Heat capacity for alloys used for cryogenic applications (after [12])
Fig. 5: Heat capacity for alloys (Al-U) used for nuclear applications (after [15])
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Heat Treatment REPORTS
his disposal. Therefore, further research work is needed.
Although the scientific study of “heat capacity” is more
than 200 years old, the actuality of this topic is stringent and
of seminal importance (fact underpinned by very numer-
ous publications) not only for aluminium or solid-state
applications, but for every material irrespective of the state
of aggregation.
LITERATURE
[1] https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRo-
cket/airplane/heat.html
[2] http://www.eoht.info/page/Specific+heat
[3] Atkins, P.; de Paula, J.: Atkins´ Physical Chemistry, 9 th Edition.
Oxford University Press, 2010
[4] http://kentchemistry.com/links/Energy/SpecificHeat.htm
[5] Agheenkov, V.G.; Ia. Ia. Mihin: Calcule Metalurgice. Bucharest:
Ed. Tehnica, 1964
[6] https://webbook.nist.gov/cgi/cbook.cgi?ID=C7429905&Units
=SI&Mask=2#Thermo -Condensed
[7] Touloukian, Y.S.; Ho, C.Y. (Eds.): Thermophysical properties of
matter. Specific Heat-Metallic Elements and Alloys 4 (1972a),
Plemnum Press, N.Y.
[8] Abu-Eishah, S.I.; Haddad, Y.; Soleiman, A.; Bajbouj, A.: A new
correlation for the specific heat of metals, metal oxides and
metal fluorides as a function of temperature, Latin American
Applied Research, 34:257-265, 2004
[9] Perry, R.H.; Green, D.W. (Eds.): Perry´s chemical engineer´s
handbook. 7 th ed., McGraw-Hill, N.Y., 1997
[10] Mc Bride, B.J.; Gordon, S.; Reno, M.A.: Coefficients for calculat-
ing thermodynamic and transport properties of individual
species. NASA Technical Memorandum 4513, 1993
[11] Kaschnitz, E.; Pabel, Th.; Funk, W.: Electrical resistivity meas-
ured by millisecond pulse-heating in comparison to thermal
conductivity of the aluminium alloy Al-7Si-0.3Mg at elevated
temperature. High Temperatures-High Pressures 43 (2014),
pp. 175–191, Old City Publishing, Inc.
[12] Simon, N.J.; Drexler, E.S.; Reed, R.P.: Review of cryogenic
mechanical and thermal properties of Al-Li-alloys and alloy
- United States Department of Commerce, 1991
[13] Corruccini, R. J.: Properties of materials at low temperatures,
Part I. Chemical Engineering Progress 53 (1957), p. 262-
[14] Unknown author: Heat capacity measurements on alumini-
um-copper and aluminium-zinc alloys
[15] International Atomic Energy Agency – Volume 4: Fuels,
IAEA-TECDOC-
[16] Branstetter, R.; Lord, A. M.; Gerstein, M.: Combustion proper-
ties of aluminum as ram-jet fuel. National Advisory Commit-
tee for Aeronautics Washington. March 28, 1951, declassified
September 10, 1954
[17] Unknown author: The thermal behavior of objects in space
[18] Niehaus, W.: Heat shield concepts and materials for reentry
vehicles. 1963
[19] https://www.hug-technik.com/inhalt/ta/metall.htm
[20] http://www2.ucdsb.on.ca/tiss/stretton/database/specific_
heat_capacity_table.html
AUTHORS
Dr. Dan Dragulin
Director Research & Development
ATC ALUVATION Technology Center
Paderborn GmbH
Marcus Rüther
Director Marketing & PR
ATC ALUVATION Technology Center
Paderborn GmbH
Table 3: E-Modulus and heat capacity at room temperature for Al, Ag, Au
[19] / [20] C at 25°C [J/g°C] E [kp/mm
2 ]
Al 0.9 6,
Ag 0.24 8,
Au 0.129 7,
