A container with an internal volume of 1 liter at 20 °C is heated to 100 °C. Find the volume of this container after heating, knowing that the coefficient of linear expansion of the material is 15 × 10⁻⁶ °C⁻¹.

Problem data:

• Initial internal volume:    V₀ = 1 ℓ;
• Initial temperature:    t_i = 20 °C;
• Final temperature:    t_f = 100 °C;
• Coefficient of linear expansion of the container:    α = 15 × 10⁻⁶ °C⁻¹.

Problem diagram:

The problem is equivalent to a body constructed of the same material as the container and of the same internal volume V₀ as the inner part of the container (Figure 1-A). When the body is heated, it will expand (Figure 1-B).


The heated body will reach a new volume V after expansion (Figure 2-A)


The internal volume of the heated container will be the same volume V as the body (Figure 2-B).

Solution

First, we convert the volume given in liters to cubic meters used in the International System of Units (S.I.) The problem gives us the coefficient of linear expansion of the material, and for the calculation of the volume expansion, we need the coefficient of volumetric expansion
The volume of the body, made of the same material as the container, after heating will be