Click save settings to reload page with unique web page address for bookmarking and sharing the current tool settings
Change the answer mode for this tool by selecting start temperature (T0), end temperature (T1), coefficient of linear thermal expansion (αL), start length (L0) or end length (L1) as the parameter to calculate instead
- Sea water temperature probe and display for depth to 100 metres
- Aquaculture submersible freshwater level & temperature transmitter
- Combined Temperature and Hydrostatic Liquid Level Sensors
- 40 ftH2O Hydroelectric power plant tail water elevation & temperature sensor
- Area thermal expansion calculations
- Volumetric thermal expansion calculations
- Isotropic length, area & volume thermal expansion calculations
- Length units conversion
- Temperature units conversion
- Temperature difference units conversion
- Thermal coefficient units conversion
This tool will calculate any parameter from the formula for linear thermal expansion L₁ = L₀·(1+αₗ·(T₁-T₀)), which includes the start temperature, end temperature, coefficient of linear thermal expansion (CLTE), start length and end length.
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.
The formulas used by this linear thermal expansion calculator to determine each individual parameter are:
T0 = T1 – (L1 / L0 – 1) / αL
T1 = T0 + (L1 / L0 – 1) / αL
αL = (L1 / L0 – 1) / (T1 – T0)
L0 = L1 / (1 + αL · (T1 – T0))
L1 = L0 · (1 + αL · (T1 – T0))
- T0 = Start temperature
- T1 = End temperature
- αL = Coefficient of linear thermal expansion (CLTE)
- L0 = Start length
- L1 = End length
Start Temperature (T0)
This is the temperature of the object before the temperature is increased.
End Temperature (T1)
This is the temperature of the object after the temperature has been increased
Coefficient Of Linear Thermal Expansion (CLTE, αL)
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 (L0)
This is the length of the object when it is at the start temperature T0 .
End Length (L1)
This is the length of the object following thermal expansion caused by an increase in temperature from T0 to T1 .
- 200cm range 0-5Vdc output submersible road flood stream depth and PT1000 sensor
- 6m range 4-20mA submersible animal feed tank level and PT100 sensor
- Water depth and temperature transmitter for 700 foot deep borehole
- Water well 30mH2Og range 4-20mA out freshwater level sensor with RTD