Thermal Expansion
The Physics Hypertextbook™
© 1998-2008 by Glenn Elert -- A Work in Progress
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Discussion
Solids
| ΔL | = | L0 | α | ΔT | linear | |
| ΔA | = | A0 | 2α | ΔT | superficial (areal) | |
| ΔL | = | L0 | 3α | ΔT | volumetric |
Liquids
ΔV = V0βΔT
Liquids have higher expansivities than solids
β ≈ 10−3/K, 3α ≈ 10−5/K
Gases
[check out the gas laws]
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 °C) | −50 | |
| carbon, graphite ⊥ | 0.5 | water, liquid (4 °C) | 0 | |
| chromium | 4.9 | water, liquid (10 °C) | 88 | |
| concrete | 8 ~ 12 | water, liquid (20 °C) | 207 | |
| copper | 16.5 | water, liquid (30 °C) | 303 | |
| germanium | 6.1 | water, liquid (40 °C) | 385 | |
| glass | 8.5 | water, liquid (50 °C) | 457 | |
| gold | 14.2 | water, liquid (60 °C) | 522 | |
| iron | 11.8 | water, liquid (70 °C) | 582 | |
| lead | 28.9 | water, liquid (80 °C) | 640 | |
| nickel | 13.3 | water, liquid (90 °C) | 695 | |
| 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 | |||
| zinc | 30.2 | |||
- "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." http://www.britishairways.com/concorde/aboutconcorde.html#facts_figures
- invar
water
- anomalous expansion of water
- ice is less dense than water
- water is most dense at 4 °C (ρ = 999.973 kg/m3)
- applications
- frozen pipes burst
- turnover of lake water in spring
Thermal Expansion of Water [magnify]
Thermal Expansion of Water [magnify]
plutonium
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.
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. [LLNL]
Thermal Expansion of Plutonium [magnify]
Summary
- bullet
Problems
practice
- Write something.
- Answer it.
- Write something else.
- Answer it.
- Write something different.
- Answer it.
- Write something completely different.
- Answer it.
numerical
- A steel bridge is built in several segments, each 20 m long. The gap between segments is 4 cm at 18 °C. What is the maximum temperature that the bridge can manage before buckling?
- Due to the high specific heat and low conductivity of water, only the
uppermost 10%
of the oceans is able to undergo any significant temperature change.
- The natural variation in ocean levels is about 10 cm from September to March. By how much does the mean temperature of the upper ocean change during this time?
- Global warming is likely to cause a rise in sea level for a number of reasons, one of which is the thermal expansion of water. Determine the rise in sea level for every 1.0 C° temperature increase in the upper ocean.
Data for the Oceans surface area 3.61 × 1014 m2 mean depth 3794 m mean temperature, overall 3.5 °C mean temperature, top 10% 10 °C - How much taller is the Eiffel Tower on the hottest day of the summer (25 °C) than the coldest day of the winter (2 °C)? The tower is 324 m tall measured from the top of the flagpole. Assume the tower is built of structural steel. (It's actually made of "puddle iron".)
Resources
- miscellaneous
- Temperature responsive self winding timepieces (US Patent 6,457,856), Steven Phillips, 28 June 2001
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