Volumetric (Cubic) Thermal Expansion
Volumetric temperature expansion calculator.
Specific volume of a unit can be expressed as
v = 1 / ρ = V / m (1)
where
v = specific volume (m^{3}/kg, ft^{3}/lb)
ρ = density (kg/m^{3}, lb/ft^{3})
V = volume of unit (m^{3}, ft^{3})
m = mass of unit (kg, lb)
The change in the units volume when temperature changes can be expressed as
dV = V_{0} β (t_{1 } t_{0}) (2)
where
dV = V_{1}  V_{0} = change in volume (m^{3}, ft^{3})
β = volumetric temperature expansion coefficient (m^{3}/m^{3 o}C, ft^{3}/ft^{3 o}F)
t_{1 }= final temperature (^{o}C, ^{o}F)
t_{0 }= initial temperature (^{o}C, ^{o}F)
The density of a fluid when temperature changes can be expressed as
ρ_{1} = m / V_{0} (1 + β (t_{1}  t_{0}))
= ρ_{0} / (1 + β (t_{1}  t_{0})) (3)
where
ρ_{1} = final density (kg/m^{3}, lb/ft^{3})
ρ_{0} = initial density (kg/m^{3}, lb/ft^{3})
Online Thermal Cubic Expansion Calculator  Expansion coefficient and Temperatures
Be aware that the expansion coefficient for some liquids  like water  may vary with temperature. The calculator below is generic and can be used for metric and imperial units as long as the use of units is consistent.
Note that the volumetric expansion coefficient used in the calculator is constant. If you want to calculate volumetric change for a liquid over a temperature range where the volumetric expansion coefficient for the liquid changes a lot  interpolate the coefficient values, or split the calculation in the different temperature ranges. Example  water is a liquid where the volumetric expansion coefficient changes a lot with temperature. Water has its highest density and smallest volume at 4^{o}C (39.2 ^{o}F). The volumetric coefficient for water is negative below 4^{o}C and indicates that the a volume decreases when temperature moves from 0^{o}C (32 ^{o}F) to 4^{o}C.
Online Thermal Cubic Expansion Calculator  Densities
This calculator can be used to calculate expansion volume when initial volume and initial and final densities for the liquid are known
V_{0}  initial volume (m^{3}, ft^{3})
ρ_{0}  initial density (kg/m^{3}, lb/ft^{3})
ρ_{1}  final density (kg/m^{3}, lb/ft^{3})
Volumetric Temperature Coefficients  β  for some Fluids
 water at 0^{o}C: 0.000050 (1/^{o}C)
 water at 4^{o}C: 0 (1/^{o}C)
 water at 10^{o}C: 0.000088 (1/^{o}C)
 water at 20^{o}C: 0.000207 (1/^{o}C)
 water at 30^{o}C: 0.000303 (1/^{o}C)
 water at 40^{o}C: 0.000385 (1/^{o}C)
 water at 50^{o}C: 0.000457 (1/^{o}C)
 water at 60^{o}C: 0.000522 (1/^{o}C)
 water at 70^{o}C: 0.000582 (1/^{o}C)
 water at 80^{o}C: 0.000640 (1/^{o}C)
 water at 90^{o}C: 0.000695 (1/^{o}C)
 ethyl alcohol: 0.00109 (1/^{ o}C), 0.00061 (1/^{o}F)
 oil: 0.00070 (1/^{o}C), 0.00039 (1/^{o}F)
Convert between Metric and Imperial Volumentric Temperature Coefficients
 1 (1/^{o}C) = 0.56 (1/^{o}F)
 1 (1/^{o}F) = 1.8 (1/^{o}C)
Example  Cubic Expansion of Oil
100 liters  0.1 m^{3}  of oil with volumetric expansion coefficient 0.00070 1/^{o}C is heated from 20^{o}C to 40^{o}C. The volumetric expansion can be calculated using equation (2)
dV = (0.1 m^{3})_{ }(0.00070 1/^{o}C) ((40 ^{o}C)  (20 ^{o}C))
= 0.0014 m^{3}
= 1.4 liter
The final volume is
100 liters + 1.4 liters = 101.4 liters
Example  Cubic Expansion of Oil
30 US gallons of oil is heated from 70^{o}F to 100^{o}F. The volumetric expansion can be calculated using equation (2)
dV = (30 gallons)_{ }(0.00039 1/^{o}F) ((100 ^{o}F)  (70 ^{o}F))
= 0.351 gallons
The final volume is
30 gallons + 0.351 gallon = 30.351 gallons
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