Physics

Superficial dilation


This form of dilation consists of a case where there is linear dilation in two dimensions.

Consider, for example, a square piece of sides that is heated a temperature , so that it is increased in size, but as there is equal expansion for both directions of the piece, it remains square, but has sides .

We can establish that:

as:

And relating to each side we can use:

So that we can analyze the surfaces, we can square the entire expression, obtaining a relationship with its areas:

But the order of magnitude of the linear expansion coefficient ) é , which when squared becomes of magnitude being immensely smaller than α. How does temperature change (Δθ) hardly exceeds a value of 10³ºC for solid state bodies, we can consider the term α²Δθ² negligible compared to 2αΔθ, which allows us to ignore it during the calculation, like this:

But considering:

Where, β is the surface expansion coefficient of each material, we have that:

Note that this equation is applicable for any geometric surface, provided that the areas are obtained through the geometric relations for each one, in particular (circular, rectangular, trapezoidal, etc.).

Example:

(1) An iron blade has dimensions 10m x 15m at normal temperature. When heated to 500ºC, what is the area of ​​this surface? Given away