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Volumetric - or Cubic Thermal Expansion

Volumetric temperature expansion with online calculator

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Specific volume of a unit can be expressed as

v = 1 / ρ = V / m                                                          (1)

where

v = specific volume (m3/kg, ft3/lb)

ρ = density (kg/m3, lb/ft3)

V = volume of unit (m3, ft3)

m = mass of unit (kg, lb)

The change in the units volume when temperature changes can be expressed as

dV = V0 β (t1 - t0)                                                        (2)

where

dV = V1 - V0 = change in volume (m3, ft3)

β = volumetric temperature expansion coefficient (m3/m3 oC, ft3/ft3 oF)

t1 = final temperature (oC, oF)

t0 = initial temperature (oC, oF)

The density of a fluid when temperature changes can be expressed as

ρ1 = m / V0 (1 + β (t1 - t0))

    = ρ0 / (1 + β (t1 - t0))                                                (3)

where

ρ1 = final density (kg/m3, lb/ft3)

ρ0 = initial density (kg/m3, lb/ft3)

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.

V0 - initial volume (m3, ft3, gallons ..)

β - volumetric temperature expansion coefficient (1/oC, 1/oF)

t0 - initial temperature (oC, oF)

t1 - final temperature (oC, oF)


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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 4oC (39.2 oF). The volumetric coefficient for water is negative below 4oC and indicates that the a volume decreases when temperature moves from 0oC (32 oF) to 4oC.

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

V0 - initial volume (m3, ft3)

ρ0 - initial density (kg/m3, lb/ft3)

ρ1 - final density (kg/m3, lb/ft3)


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Volumetric Temperature Coefficients - β - for some Fluids

  • water at 0oC: -0.000050 (1/oC)
  • water at 4oC: 0 (1/oC)
  • water at 10oC: 0.000088 (1/oC)
  • water at 20oC: 0.000207 (1/oC)
  • water at 30oC: 0.000303 (1/oC)
  • water at 40oC: 0.000385 (1/oC)
  • water at 50oC: 0.000457 (1/oC)
  • water at 60oC: 0.000522 (1/oC)
  • water at 70oC: 0.000582 (1/oC)
  • water at 80oC: 0.000640 (1/oC)
  • water at 90oC: 0.000695 (1/oC)
  • ethyl alcohol: 0.00109 (1/ oC), 0.00061 (1/oF)
  • oil: 0.00070 (1/oC), 0.00039 (1/oF)

Convert between Metric and Imperial Volumentric Temperature Coefficients

  • 1 (1/oC) =  0.56 (1/oF)
  • 1 (1/oF) =  1.8 (1/oC)

Example - Cubic Expansion of Oil

100 liters - 0.1 m3 - of oil with volumetric expansion coefficient 0.00070 1/oC is heated from 20oC to 40oC. The volumetric expansion can be calculated using equation (2)

dV = (0.1 m3) (0.00070 1/oC) ((40 oC) - (20 oC)) 

  = 0.0014 m3

  = 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 70oF to 100oC. The volumetric expansion can be calculated using equation (2)

dV = (30 gallons) (0.00039 1/oF) ((100 oF) - (70 oF)) 

    = 0.351 gallons

The final volume is

30 gallons + 0.351 gallon = 30.351 gallons

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