Volumetric Temperature Expansion

Cubical expansion when changing temperature

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)

Volumetric Temperature Coefficients - β - of some common Fluids

• water : 0.00021 (m³/m^{3 o}C)
• ethyl alcohol : 0.00109 (m³/m^{3 o}C)
• oil : 0.00063 (m³/m^{3 o}C)

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