To calculate the real cubic expansivity of the liquid, we can use the formula for cubic expansion:
β = (ΔV / V₀) / ΔT
where:
- β = cubic expansivity
- ΔV = change in volume
- V₀ = original volume
- ΔT = change in temperature
First, we need to find the change in density and then relate that to volume change:
The density of the liquid at 0°C is 44.25 g and at 50°C is 42.02 g. From density, we can find the volume using the formula:
V = m / ρ
Let’s assume we have 1 g of the liquid to simplify calculations:
At 0°C:
V₀ = 1 g / 44.25 g/cm³ = 0.0226 cm³
At 50°C:
V₁ = 1 g / 42.02 g/cm³ = 0.0238 cm³
The change in volume (ΔV) is:
ΔV = V₁ – V₀ = 0.0238 cm³ – 0.0226 cm³ = 0.0012 cm³
The change in temperature (ΔT) is:
ΔT = 50°C – 0°C = 50°C
Now, we can substitute our values into the cubic expansivity formula:
β = (0.0012 cm³ / 0.0226 cm³) / 50°C
β = 0.00053 cm³/cm³/°C or 5.3 x 10⁻⁴ °C⁻¹
This value represents the real cubic expansivity of the liquid under the given conditions.
Note: To adjust for the linear expansivity of the glass, you can consider that the volumetric expansion coefficient of the glass can also add to the overall behavior in practical applications. This should be taken into account when calculating for systems involving both liquids and solids.