The Physics
Opus in profectus

Thermal Expansion

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For many solids, expansion is directly proportional to temperature change.

∆ℓ = αℓ0T

Areas expand twice as much as lengths do.

A = 2αA0T

Volumes expand three times as much as lengths do.

V = 3αV0T


measurement techniques

anisotropic expansion


Liquids can only expand in volume.

V = βV0T

Liquids have higher expansivities than solids.

β~10−3/K, 3α~10−5/K


Coefficients of linear thermal expansion
material α (10−6/K)
alumina (αAl2O3) 5.30
aluminium 23.1
barium ferrite 10
brass 20.3
carbon, diamond 1.18
carbon, graphite ∥ 6.5
carbon, graphite ⊥ 0.5
chromium 4.9
concrete 8–12
copper 16.65
epoxy 55
germanium 6.1
glass, typical 8.5
glass, ultra-low expansion 0.04
gold 14.2
invar (64% Fe, 36% Ni) 1.2
iron 11.8
lead 28.9
nickel 13.3
plastics 40–120
plexiglas 93
platinum 8.8
plutonium 54
silicon 4.68
silver 18.9
solder, lead-tin 25
steel, stainless 17.3
steel, structural 12
tin 22
titanium 8.5
tungsten 4.5
uranium 13.9
water, ice (0 °C) 51
wood (lumber), tangential 36
wood (lumber), radial 26
wood (lumber), axial 3.7
zinc 30.2
zirconium tungstate (ZrW2O8) −8.8
Coefficients of volume thermal expansion ☞ All values in both tables are averages for temperatures centered near 20 °C unless otherwise stated.
material β (10−6/K)
alcohol, ethyl 1120
gasoline 950
jet fuel, kerosene 990
mercury 181
water, liquid (1 °C) −50
water, liquid (4 °C) 0
water, liquid (10 °C) 88
water, liquid (20 °C) 207
water, liquid (30 °C) 303
water, liquid (40 °C) 385
water, liquid (50 °C) 457
water, liquid (60 °C) 522
water, liquid (70 °C) 582
water, liquid (80 °C) 640
water, liquid (90 °C) 695


Line graph

Line graph


Plutonium undergoes more phase transitions at ordinary pressures than any other element. As plutonium is heated it transforms through six different crystal structures before melting — α [alpha], β [beta], γ [gamma], ∆ [delta], ∆′ [delta prime], and ε [epsilon]. Physical properties like density and thermal expansion vary significantly from phase to phase making it one of the more difficult metals to machine and work. The metallurgy of plutonium is best left to the experts.

Notes form LLNL that must be paraphrased. "One of plutonium's unique physical properties is that the pure metal exhibits six solid-state phase transformations before reaching its liquid state, passing from alpha, beta, gamma, delta, delta-prime, to epsilon. Large volume expansions and contractions occur between the stable room-temperature alpha phase and the element's liquid state. Another unusual feature is that unalloyed plutonium melts at a relatively low temperature, approximately 640 °C, to yield a liquid of higher density than the solid from which it melts. In addition, the elastic properties of the delta face-centered cubic (fcc) phase of plutonium are highly directional (anisotropic). That is, the elasticity of the metal varies widely along different crystallographic directions by as much as a factor of six to seven."


Line graph


Behavior of gases is more complicated, gases will expand as much as pressure will allow. Check out the gas laws.

PV = nRT PV = NkT