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Thermal Expansion


 Thermal Expansion

ΔL      =      L0     α     ΔT           linear
ΔA      =      A0     2α     ΔT           areal
ΔL      =      L0     3α     ΔT           volumetric

    "What's more, the aircraft expands by 15-25 centimetres during flight because of the scorching heat created by friction with air. Designers used rollers to isolate the cabin from the body, so that stretching doesn't rip the plane apart." Helen Pearson "Concorde wings its way into retirement." Nature Physics Portal. October 2003.
    "Concorde measures 204ft in length - stretching between six and ten inches in-flight due to heating of the airframe. She is painted in a specially developed white paint to accommodate these changes and to dissipate the heat generated by supersonic flight." source


ΔV = βV0ΔT

Liquids have higher expansivities than solids

β ≈ 10−3/K, 3α ≈ 10−5/K


behavior of gases is more complicated, gases will expand as much as pressure will allow
Coefficients of Thermal Expansion for Selected Materials
material     linear
α (10−6 K−1)           material     volume
β (10−6 K−1)
aluminium     23.1           alcohol, ethyl     1120
barium ferrite     10           gasoline     950
brass     20.3           jet fuel, kerosene     990
carbon, diamond     1.18           mercury     181
carbon, graphite ∥     6.5           water, liquid (1 ℃)     −50
carbon, graphite ⊥     0.5           water, liquid (4 ℃)     0
chromium     4.9           water, liquid (10 ℃)     88
concrete     8 ~ 12           water, liquid (20 ℃)     207
copper     16.5           water, liquid (30 ℃)     303
germanium     6.1           water, liquid (40 ℃)     385
glass     8.5           water, liquid (50 ℃)     457
gold     14.2           water, liquid (60 ℃)     522
invar (64% Fe, 36% Ni)     1.2           water, liquid (70 ℃)     582
iron     11.8           water, liquid (80 ℃)     640
lead     28.9           water, liquid (90 ℃)     695
nickel     13.3                
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 ℃)     51                
zinc     30.2                

    anomalous expansion of water
        ice is less dense than water
        water is most dense at 4 ℃ (ρ = 999.973 kg/m3)
        frozen pipes burst
        turnover of lake water in spring


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], Δ [delta], Δ′ [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 ℃, 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"

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