Specific
Heat| Specific
Heat |
In General > s.a. heat.
* History: Einstein's
1907 article on the specific heat of solids introduced for the first time the
effect of lattice vibrations in the thermodynamic properties of crystals; The
next important step was the introduction of Debye's model.
* Heat capacity: The
quantity C:= 
U/T,
calculated either at constant volume or at constant pressure, if appropriate;
When the two are different, Cp is
greater
than CV because of the extra
work the
system
does in the expansion, but for a solid there is only one notion.
* Specific heat:
The heat capacity per mole c = C/n, with n the number of moles, or per unit
mass, c' = C/m.
Specific Systems > s.a. ising
model.
* Classical gas: Heat
capacity CV =
(3/2) Nk [monatomic]; Specific heat c = (3/2)
ln(m/2
2)
+ (5/2).
* Black hole: It is negative (as is typical for a self-gravitating
system, since there can be no equilibrium with an infinite thermal bath),
and
given
by
CS = T (S/T)
= (M/T)
= –8M 2
= –TH2/8 .
@ Solid: Einstein AdP(07); Shubin & Sunada mp/05 [geometric
approach].
@ Black hole: Gibbons & Perry PRS(78) [thermal Green's functions];
Gorski & Mazur ht/97 [quantum
effects, positive].
@ Boson system:
Wang AJP(04)
[above condensation T]; Ramakumar & Das PLA(06)
[on a lattice].
@ Self-gravitating: Lynden-Bell & Wood MNRAS(67), Lynden-Bell cm/98-in.
@ Other systems: Albuquerque et al PhyA(04)
[quasi-periodic structures, oscillatory
c(T)]; Moreira & Oliveira PRA(06)gq
[relativistic particle
on a cone].
Special Concepts and Results > s.a. sound [speed].
* Negative: In addition to gravitating systems, it can happen with
small numbers of particles, or some non-ergodic systems.
* Dulong-Petit law:
The universality of specific heats of solids at high
temperature, stating that C = 5.94 cal/K per mole; It breaks down
at low T (say,
below 600 K or so, but it depends on the material), when equipartition no longer
holds; > s.a Wikipedia page.
* Einstein model: Atoms
are treated as non-interacting harmonic oscillators, so the density of states
is a delta function at a single frequency; > s.a. Wikipedia
page.
* Debye model: The density
of states for atomic vibrations is modeled as g(
)
= const 2,
up to some H;
This corresponds to a constant speed of sound, and gives C proportional
to T 3;
> s.a. scienceworld page, Wikipedia page.
@ Negative: Antoni et al cm/99-in
[N-body];
Schmidt et al PRL(01)
+ pn(01)feb
[Na clusters]; Thirring et al
PRL(03)
[non-ergodic]; Einarsson PLA(04)gq [conditions];
Posch & Thirring PRL(05)
[and stellar stability]; Rao et al AP(08) [particles in box with potential
well].
@ In non-extensive statistics: Lenzi et al PLA(02); Álvarez-Ramírez
et al PLA(05).
@ Related topics: Gearhart AJP(96)
[and equipartition]; Pizarro et al AJP(96);
Filardo
Bassalo et al NCB(01) [dissipative]; Fraundorf AJP(03);
Behringer et al JPA(05)
[microcanonical, finite size].
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
8 jun 2008