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# Linear Thermal Expansion

## Linear temperature expansion - online calculator

When an object is heated or cooled, its length changes by an amount proportional to the original length and the change in temperature. The linear thermal expansion - the change in length - of an object can be expressed as

dl = L0 α (t1 - t0)                                (1)

where

dl = change in object length (m, inches)

L0 = initial length of object (m, inches)

α =  linear expansion coefficient (m/moC, in/inoF)

t0 = initial temperature (oC, oF)

t1 = final temperature (oC, oF)

The final length of the object can be calculated as

L1 = L0 + dl

= L0 + L0 α (t1 - t0)                                (2)

where

L1 = final length of object (m, inches)

Note! - linear expansion coefficients for most materials varies with temperature.

For wider temperature ranges - calculate for smaller spans and integrate the results.

### Online Thermal Linear Expansion Calculator

L0 - initial length of object (m, inches)

α - linear expansion coefficient (m/moC, in/inoF)

t0 - initial temperature (oC, oF)

t1 - final temperature (oC, oF)

#### Linear Temperature Coefficients - α - for some common metals

• aluminum : 0.000023 (m/moC) (23 μm/moC)
• steel: 0.000012 (m/moC) (12 μm/moC)
• copper: 0.000017 (m/moC) (17 μm/moC)
• more coefficients ..
• more metals ..

### Example - Expansion of an Aluminum Beam

An aluminum construction is designed for temperatures ranging -30oC to 50oC. If a beam's length is 6 m when assembled at 20oC - the shortest final length of the beam at minimum temperature -30oC can be calculated as

L1 = (6 m) + (6 m) (0.000023 m/moC) ((-30 oC) - (20 oC))

=  5.993 m

The longest final length of the beam at maximum temperature 50oC can be calculated as

L1 = (6 m) + (6 m) (0.000023 m/moC) ((50 oC) - (20 oC))

=  6.004 m

### Superficial Expansion

The amount by which a unit area of a material increases when the temperature is raised by one degree is called the coefficient of superficial (area) expansion.

### Cubic Expansion

The amount by which a unit volume of a material increases when the temperature is raised by one degree is called the coefficient of cubic expansion.

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Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

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