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)
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)
ρ 1 = final density (kg/m 3 , lb/ft 3 )
ρ 0 = initial density (kg/m 3 , lb/ft 3 )
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 .
This calculator can be used to calculate expansion volume when initial volume and initial and final densities for the liquid are known
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
30 US gallons of oil is heated from 7 0 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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