We know that liquids swell by obeying the same laws that we study for solids. However, as liquids do not have their own shape, but take the shape of the container, only the study of their volumetric expansion has meaning.
When the expansion of a liquid is observed, it must be contained in a flask that is heated simultaneously with it. Thus, both will dilate, and as the capacity of the vial increases, the dilation we will see, for the liquid, will be an apparent dilation. The actual liquid dilation will be greater than the apparent dilation observed.
This actual expansion is, of course, equal to the sum of the apparent expansion and the volumetric expansion of the container. When using a container whose coefficient of expansion is very small, the liquid's apparent expansion becomes practically equal to its actual expansion.
Suppose that, in an experiment, the liquid under study completely fills the container in the initial situation. For practical purposes, we will consider that the initial volume of liquid may leak out as a result of the dilation.
The apparent dilatation of the liquid is also proportional to the initial volume, VO and temperature variation, Δθ, so that:
In this expression, Yapparent is the coefficient of expansion of the liquid. We also know that the variation in the volume of the bottle is:
Naturally, the actual increase in liquid volume must correspond to the volume of overflowed liquid plus the increase in the volume of the bottle. In other words, the actual increase in liquid volume corresponds to the amount of liquid that spills, plus the amount of liquid that would overflow if the container (flask) did not suffer any dilation. Thus, we have:
From this equation, we can get:
This expression allows us to conclude that the apparent expansion of a liquid depends on the nature of the liquid and the container in which it is placed to be heated.
Domitian Marques
Graduated in Physics
Source: Brazil School - https://brasilescola.uol.com.br/fisica/dilatacao-aparente.htm
