Thermal Expansion - Volumetric or Cubic

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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)

ρ = density (kg/m³)

V = volume of unit (m³)

m = mass of unit (kg)

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

dV = V₀ β (t₁ - t₀)          (2)

where

dV = V₁ - V₀ = change in volume (m³)

β = volumetric temperature expansion coefficient (m³/m^{3 o}C)

t₁ = final temperature (^oC)

t₀ = initial temperature (^oC)

The density of a fluid when the temperature is changed can be expressed as

ρ₁ = m / V₀ (1 + β (t₁ - t₀))

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

where

ρ₁ = final density (kg/m³)

ρ₀ = initial density (kg/m³)

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Volumetric Temperature Coefficients - β - of some common Fluids

• water : 0.000214 (1/^oC),
  
• ethyl alcohol : 0.00109 (1/ ^oC), 0.00061 (1/^oF)
• oil : 0.00070 (1/^oC), 0.00039 (1/^oF)

• Volumetric expansion coefficients of some common fluids

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