Calculate Isotropic Material Thermal Expansion Parameters  

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Change the answer mode for this tool by selecting start temperature (T_{0}), end temperature (T_{1}), coefficient of linear thermal expansion (α_{L}), start length (L_{0}), end length (L_{1}), start area (A_{0}), end area (A_{1}), start volume (V_{0}) or end volume (V_{1}) as the parameter to calculate instead
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User Guide
This tool will calculate any parameter from the formula for length, area or volume thermal expansion for an isotropic material, which includes the start temperature, end temperature, coefficient of linear thermal expansion (CLTE), start length, end length, start area, end area, start volume and end volume.
The linear thermal expansion formula is used to calculate the change in length of an object, due to a change in temperature. It has been widely proven and accepted by the scientific and engineering community that in many cases the change in length to overall length ratio is directly proportional to the change in temperature of the object. However, it is only an approximation, and will only produce a precise value if the change in length is small compared to the overall length of an object, and the thermal coefficient of expansion of the material does not change by much, within the range of temperature change.
For an isotropic material which expands by the same degree in all directions, the coefficient for linear thermal expansion can also be used to derive the coefficient for area & volumetric thermal expansion, by multiplying the coefficient by 2 and 3 respectively.
Formulas
The formulas used by this length, area and volume isotropic thermal expansion calculator to determine each individual parameter are:
T_{0} = T_{1} – (L_{1} / L_{0} – 1) / α_{L
}T_{0} = T_{1} – (A_{1} / A_{0} – 1) / (2 · α_{L})
T_{0} = T_{1} – (V_{1} / V_{0} – 1) / (3 · α_{L})
T_{1} = T_{0} + (L_{1} / L_{0} – 1) / α_{L
}T_{1} = T_{0} + (A_{1} / A_{0} – 1) / (2 · α_{L})
T_{1} = T_{0} + (V_{1} / V_{0} – 1) / (3 · α_{L})
α_{L} = (L_{1} / L_{0} – 1) / (T_{1} – T_{0})
α_{L} = (A_{1} / A_{0} – 1) / (2 · (T_{1} – T_{0}))
α_{L} = (V_{1} / V_{0} – 1) / (3 · (T_{1} – T_{0}))
L_{0} = L_{1} / (1 + α_{L} · (T_{1} – T_{0}))
L_{1} = L_{0} · (1 + α_{L} · (T_{1} – T_{0}))
A_{0} = A_{1} / (1 + 2 · α_{L} · (T_{1} – T_{0}))
A_{1} = A_{0} · (1 + 2 · α_{L} · (T_{1} – T_{0}))
V_{0} = V_{1} / (1 + 3 · α_{L} · (T_{1} – T_{0}))
V_{1} = V_{0} · (1 + 3 · α_{L} · (T_{1} – T_{0}))
Symbols
 T_{0} = Start temperature
 T_{1} = End temperature
 α_{L} = Coefficient of linear thermal expansion (CLTE)
 L_{0} = Start length
 L_{1} = End length
 A_{0} = Start area
 A_{1} = End area
 V_{0} = Start volume
 V_{1} = End volume
Start Temperature (T_{0})
This is the temperature of the object before the temperature is increased.
End Temperature (T_{1})
This is the temperature of the object after the temperature has been increased
Coefficient Of Linear Thermal Expansion (CLTE, α_{L})
This is a fixed value which is used to determine how much a small change in temperature will affect the length of a particular substance. The coefficient defines the fractional change in length of a substance per unit change in its temperature.
Start Length (L_{0})
This is the length of the object when it is at the start temperature T_{0} .
End Length (L_{1})
This is the length of the object following thermal expansion caused by an increase in temperature from T_{0} to T_{1} .
Start Area (A_{0})
This is the two dimensional area of a region on the object when it is at the start temperature T_{0} .
End Area (A_{1})
This is the two dimensional area of a region on the object following thermal expansion caused by an increase in temperature from T_{0} to T_{1} .
Start Volume (V_{0})
This is the three dimensional volume of the object when it is at the start temperature T_{0} .
End Volume (V_{1})
This is the three dimensional volume of the object following thermal expansion caused by an increase in temperature from T_{0} to T_{1} .
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