# Thermal Expansion Coefficient

on . Posted in Thermodynamics

Thermal expansion coefficient, abbreviated as $$\alpha$$ (Greek symbol alpha), also called coefficient of thermal expansion, and linear thermal expansion coefficient, is the percentage change in the length of the material per degree of temperature change, heated solid or liquid.  It is a material property that quantifies how much a material expands or contracts when its temperature changes.  When a material is heated, its particles gain kinetic energy and move more vigorously, causing them to spread out and increase the material's overall volume.  Similarly, when a material is cooled, its particles lose kinetic energy and become less active, leading to a decrease in volume.

The thermal expansion coefficient is defined as the fractional change in size (length, area, or volume) of a material per unit change in temperature.

Different materials have different thermal expansion coefficients, meaning they will expand or contract by varying amounts for the same change in temperature.  For example, metals generally have higher thermal expansion coefficients compared to ceramics.  This property is essential to consider in various engineering applications, such as when designing structures that experience temperature variations to ensure that they can withstand the resulting dimensional changes without causing issues or failures.

### Thermal Expansion Coefficient formula

$$\alpha = l_f - l_i \;/\; l_i \; ( T_f - T_i )$$     (Thermal Expansion Coefficient)

$$l_f = \alpha \; l_i \; ( T_f - T_i ) + l_i$$

$$l_i = l_f \;/\; \alpha \; \left( T_f - T_i \right) + 1$$

$$T_f = ( l_f - l_i \;/\; \alpha \; l_i ) + T_i$$

$$T_i = ( l_f - l_i \;/\; \alpha \; l_i ) - T_f$$

Symbol English Metric
$$\alpha$$  (Greek symbol alpha) = thermal expansion coefficient  $$in \;/\; in\;F$$ $$mm \;/\; mm\;C$$
$$l_f$$ = final length $$in$$ $$mm$$
$$l_i$$ = initial length $$in$$ $$mm$$
$$T_f$$ = final temperature $$F$$ $$C$$
$$T_i$$ = initial temperature $$F$$ $$C$$

### Thermal Expansion Coefficient of material

Material

Coefficient of Expansion in

inches of expansion per inch

of material per degree F

ABS plastics, glass fiber-reinforced 0.0000170
ABS plastics 0.0000410
Acrylic, extruded 0.0001300
Acrylic, sheet cast 0.0000410
Aluminum 0.0000131
Arsenic 0.0000026
Barium 0.0000114
Beryllium 0.0000067
Brass, red 0.0000090
Brass, yellow 0.0000010
Brick, masonry 0.0000031
Bronze 0.0000100
Borosilicate, Glass 0.0000018
Cadmium 0.0000168
Calcium 0.0000124
Carbon, Diamond 0.0000050
Carbon Steel 0.0000067
Cast Iron 0.0000059
Cellulose Acetate (CA) 0.0000722
Cellulose Acetate Butyrate (CAB) 0.0000140
Cellulose Nitrate (CN) 0.0000556
Cement 0.0000060
Cerium 0.0000029
Chlorinated Polyvinylchloride (CPVC) 0.0000370
Chromium 0.0000033
Clay Tile 0.0000033
Cobalt 0.0000067
Concrete 0.0000080
Concrete Structure 0.0000055
Constantan 0.0000104
Copper 0.0000098
Diamond 0.0000006
Ductile Iron 0.0000056
Dysprosium 0.0000055
Ebonite 0.0000428
Epoxy 0.0000310
Erbium 0.0000068
Ethylene Ethyl Acrylate (EEA) 0.0000114
Ethylene Vinyl Acetate (EVA) 0.0000100
Europium 0.0000194
Fibre-reinforced Plastic (FRP), Epoxy 0.0000120
Fibre-reinforced Plastic (FRP), Polyester 0.0000170
Fibre-reinforced Plastic (FRP), Vinyl Ester 0.0000100
Fluorinated Ethylene Propylene (FEP) 0.0000050
Fluoroethylene Propylene (FEP) 0.0000750
Gadolinium 0.0000050
Germanium 0.0000034
Glass, hard 0.0000033
Glass, plate 0.0000050
Glass, Pyrex 0.0000022
Gold 0.0000079
Granite 0.0000044
Graphite 0.0000044
Hafnium 0.0000033
Hastelloy C 0.0000053
High-density Polyethylene (HDPE) 0.0001100
Holmium 0.0000062
Ice 0.0000280
Incoloy 0.0000080
Inconel 0.0000064
Indium 0.0000183
Invar 0.0000008
Iridium 0.0000033
Iron, pure 0.0000067
Iron, forged 0.0000063
Lanthanum 0.0000067
Lead 0.0000151
Limestone 0.0000044
Lithium 0.0000256
Lutetium 0.0000055
Magnesium 0.0000140
Manganese 0.0000120
Manganese, Bronze 0.0000118
Marble 0.0000031 - 0.0000079
Masonry 0.0000026 - 0.0000050
Mica, Wrought 0.0000017
Molybdenum, Wrought 0.0000030
Monel 0.0000078
Mortar 0.0000041 - 0.0000075
Neodymium 0.0000053
Nickel 0.0000072
Nickel, Wrought 0.0000074
Nylon, general purpose 0.000040
Nylon, type 11 0.0000556
Nylon, type 12 0.0000447
Nylon, type 6 cast 0.0000472
Osmium 0.0000028
Palladium 0.0000066
Plaster 0.0000092
Platinum 0.0000050
Plutonium 0.0000198
Polyallomer (PA) 0.0000508
Polyamide (PA) 0.0000611
Polyaryletherketone (PAEK) 0.0000230
Polycarbonate (PC) 0.0000390
Polycarbonate (PC), glass fiber-reinforced 0.0000120
Polyester 0.0000690
Polyester, glass fiber-reinforced 0.0000140
Polyethylene (PE) 0.0001110
Polyether Ether Ketone (PEEK) 0.0000260
Polyethylene Terephthalate (PET) 0.0000330
Polyphenylene (PPE), glass fiber-reinforced 0.0000200
Polypropylene (PP), glass fiber-reinforced 0.0000180
Polypropylene (PP), unfiltered 0.0000503
Polystyrene (PS) 0.0000389
Polysulfone (PSO) 0.0000310
Polytetrafluoroethylene (PTFE) 0.0000380
Polyurethane (PUR), rigid 0.0000320
Polyvinyl Chloride (PVC) 0.0000280
Polyvinylidene Fluoride (PVDF) 0.0000710
Quartz 0.00000043 - 0.00000079
Red Brass 0.0000104
Rhenium 0.0000037
Rhodium 0.0000044
Rubber, hard 0.0000328
Ruthenium 0.0000051
Samarium 0.0000071
Sandstone 0.0000065
Saran 0.0000380
Scandium 0.0000057
Selenium 0.0000021
Silicon 0.0000028
Silver 0.0000107
Slate 0.0000058
Stainless Steel 304 (Austenitic) 0.0000096
Stainless Steel 310 (Austenitic) 0.0000080
Stainless Steel 316 (Austenitic) 0.0000089
Stainless Steel 410 (Ferritic) 0.0000089
Steel 0.0000073
Styrene 0.0000600
Terne 0.0000065
Thallium 0.0000166
Thorium 0.0000067
Thulium 0.0000074
Tin 0.0000128
Titanium 0.0000048
Tungsten 0.0000025
Uranium 0.0000074
Vanadium 0.0000044
Wood, Fir 0.0000021
Wood, Oak 0.0000030
Wood, Pine 0.0000028
Zinc 0.0000165