Dilatação Superficial e Volumétrica - Brasil Escola

Summary

In this physics lesson, Professor Joab explains the concepts of thermal expansion, including superficial and volumetric dilation. He illustrates how materials expand when heated, with molecular vibrations causing the molecules to move apart. He covers how superficial expansion occurs in two dimensions, such as in tiles or metal plates, and provides formulas to calculate area changes based on temperature variation. The lesson also delves into volumetric expansion, where the material's volume increases due to temperature rise. Through practical examples and calculations, the video clarifies how coefficients of linear, superficial, and volumetric dilations are used in real-world scenarios.

Takeaways

• 😀 Dilatation occurs when materials are subjected to temperature changes, causing molecular vibrations that lead to expansion or contraction.
• 😀 Thermal expansion leads to the separation of molecules, causing the material to expand, while cooling causes contraction due to reduced molecular vibration.
• 😀 Superficial (area) expansion occurs in two dimensions and can be calculated by the formula: ΔA = β * A0 * ΔT.
• 😀 The coefficient of superficial expansion (β) is twice the linear coefficient of expansion (α) of the material.
• 😀 The expansion of materials in two dimensions, such as tiles or metal sheets, can be considered bidimensional, making it a superficial dilatation.
• 😀 To calculate the increase in area, you multiply the initial area (A0) by the coefficient of superficial expansion (β) and the temperature change (ΔT).
• 😀 When calculating the percentage increase in area, you multiply the increase by 100 to find the percentage relative to the initial area.
• 😀 Volumetric expansion occurs in three dimensions and can be calculated using the formula: ΔV = γ * V0 * ΔT, where γ is the volumetric expansion coefficient.
• 😀 The coefficient of volumetric expansion (γ) is three times the linear coefficient of expansion (α) of the material.
• 😀 To find the temperature required for a specific volumetric expansion, the change in temperature (ΔT) is calculated based on the desired percentage change in volume.
• 😀 Example problems demonstrate the application of these formulas for calculating the area and volume changes in materials subjected to temperature variations.

Q & A

What is thermal expansion and contraction?

Thermal expansion occurs when a material is heated, causing its temperature to rise. This increase in temperature leads to more intense molecular vibrations, causing the molecules to move farther apart and the material to expand. On the other hand, thermal contraction happens when a material is cooled, decreasing its temperature and causing the molecules to move closer together, resulting in a reduction in size.

What is superficial (2D) thermal expansion?

Superficial thermal expansion refers to the expansion that occurs in two dimensions, or in the area, of a material. This is commonly observed in objects like tiles, metal sheets, or thin materials, where the third dimension (thickness) is negligible, and only the area changes due to temperature variations.

How is the increase in area due to temperature change calculated?

The increase in area (ΔA) is calculated using the equation ΔA = A₀ * β * ΔT, where A₀ is the initial area, β is the coefficient of superficial thermal expansion, and ΔT is the change in temperature. The coefficient β is twice the value of the linear thermal expansion coefficient (α).

What does the symbol β represent in the context of superficial expansion?

The symbol β represents the coefficient of superficial (2D) thermal expansion. It is related to the linear thermal expansion coefficient (α) by the equation β = 2α, meaning that the superficial expansion coefficient is twice as large as the linear expansion coefficient.

How does the temperature change affect the area of a material?

As the temperature of a material increases, its molecules vibrate more intensely, causing them to move farther apart. This leads to an increase in the material's area. The extent of this area increase is directly proportional to the change in temperature and the material's initial area.

How is the percentage increase in area due to thermal expansion calculated?

To calculate the percentage increase in area, the equation for the change in area (ΔA) is used, and then the result is multiplied by 100 to obtain the percentage. For example, if the change in area is ΔA = A₀ * 10^-3, multiplying this by 100 gives the percentage increase.

What is volumetric thermal expansion, and how does it differ from superficial expansion?

Volumetric thermal expansion occurs when a material expands in three dimensions (length, width, and height), as opposed to superficial expansion, which occurs in two dimensions (area). This type of expansion is observed in solid objects like cubes or spheres, where the entire volume increases as the temperature rises.

How is the change in volume calculated for a material experiencing thermal expansion?

The change in volume (ΔV) due to thermal expansion is calculated using the equation ΔV = V₀ * γ * ΔT, where V₀ is the initial volume, γ is the coefficient of volumetric thermal expansion, and ΔT is the change in temperature. The coefficient γ is three times the value of the linear thermal expansion coefficient (α).

What is the relationship between the coefficients of linear, superficial, and volumetric thermal expansion?

The coefficients of thermal expansion are related by the following: the coefficient of superficial expansion (β) is twice the coefficient of linear expansion (α), and the coefficient of volumetric expansion (γ) is three times the coefficient of linear expansion (α). These relationships account for the expansion in different dimensions—one-dimensional, two-dimensional, and three-dimensional.

What is the required temperature change for a metallic sphere to increase its volume by 1.2%?

For a metallic sphere with a linear expansion coefficient of 2 x 10^-5, to achieve a 1.2% increase in volume, the temperature must be raised by 200°C. This can be calculated using the equation for volumetric expansion, and solving for the temperature change (ΔT).