Um recipiente tem capacidade de 3.000 cm3 a 20 °C e está completamente cheio de um determinado líquido. Ao aquecer o conjunto até 120 °C, transbordam 27 cm3. O coeficiente de dilatação aparente desse líquido, em relação ao material de que é feito o recipiente é, em °C–1, igual a

Let's break down the problem step by step. We have a container with a capacity of 3000 cm³ at 20°C, completely filled with a certain liquid. When heated to 120°C, 27 cm³ overflow. We need to find the apparent coefficient of expansion of the liquid with respect to the material of the container, in °C⁻¹.

First, let's analyze the situation: the liquid expands when heated, causing it to overflow. This means that the volume of the liquid at 120°C is greater than its initial volume at 20°C.

Now, let's use the formula for thermal expansion of liquids:

ΔV = V₀ × β × ΔT

where ΔV is the change in volume, V₀ is the initial volume, β is the coefficient of expansion, and ΔT is the change in temperature.

We know that the initial volume is 3000 cm³, and the volume at 120°C is 3000 cm³ + 27 cm³ = 3027 cm³. The change in temperature is ΔT = 120°C - 20°C = 100°C.

Substituting the values, we get:

27 cm³ = 3000 cm³ × β × 100°C

Now, we can solve for β:

β = 27 cm³ / (3000 cm³ × 100°C) = 9.0 × 10⁻⁵ °C⁻¹

Therefore, the correct answer is B) 9.0 × 10⁻⁵ °C⁻¹.

This result makes sense, as the coefficient of expansion is expected to be a small value, indicating that the liquid expands only slightly with an increase in temperature.