Introduction to Superficial Expansion

Relevance of the Topic

Thermal expansion, a phenomenon studied in this chapter, is a physical property that directly affects the dimensions of any substance. The study of superficial expansion is a natural extension of this phenomenon, which, in addition to influencing the volume of objects, also affects their surface area.

Understanding superficial expansion is essential to comprehend the occurrence of everyday phenomena, such as glass breakage in sun-exposed facades, or the fitting of lids on glass jars after sterilization, for example. It is also fundamental in the development of technologies and in engineering, in areas such as the manufacturing of metal structures or the construction of electronic circuits.

Contextualization

In the curriculum scope, the study of superficial expansion is placed right after the study of linear expansion, as superficial expansion is a direct consequence of linear expansion. The expansion laws are fundamental for the understanding of later thermodynamics concepts and material structures, thus becoming a crucial step in the teaching of physics.

Furthermore, the Physics discipline in the 2nd year of High School is the foundation for further studies in engineering, chemistry, and physics, making the mastery of this topic even more relevant. Therefore, the study of Superficial Expansion is a necessary preparation to understand more complex concepts in the future.

Theoretical Development

Components

• Superficial Expansion: Defined as the variation in the area of a body when it is subjected to heating or cooling. The concept of superficial expansion is essentially the same as linear expansion, but applied to the area instead of length. It is, therefore, a physical property of matter that highlights the alteration of bodies' dimensions when their temperature changes.

• Law of Superficial Expansion: In its most basic form, the law of superficial expansion, also known as Gay-Lussac's law, establishes that the variation in area of a body is proportional to its initial area and the temperature variation it is subjected to. It can be expressed by the formula ΔA = γ * A * ΔT, where ΔA is the variation in area, γ is the coefficient of superficial expansion, and ΔT is the temperature variation.

• Coefficient of Superficial Expansion: This coefficient, represented by γ, is a quantity that expresses the relative variation in area of a body for each degree Celsius (or Kelvin) of temperature variation. In other words, it indicates how much the body's area changes when its temperature changes. Each material has its own coefficient of superficial expansion, which can vary with temperature.

Key Terms

• Initial Area (A): The area that an object has before undergoing expansion.

• Variation in Area (ΔA): The difference between the final area and the initial area of the object after expansion.

• Temperature Variation (ΔT): The difference between the final temperature and the initial temperature of the object.

Examples and Cases

• Suspension Bridge Design: Engineers responsible for the construction of suspension bridges must take into account the expansion and contraction of the steel cables used for support. The expansion coefficients of these cables must be carefully considered during the design to avoid structural problems.

• Door Locks on Hot Days: On very hot days, it is common to notice the difficulty some people have when trying to open the house door using the key. This occurs due to the expansion of the lock, which makes the internal space of the lock smaller, thus making it difficult to fit the key.

• Installation of Glass Panes in Windows: During the installation of glass panes in windows, it is important to leave a small free space between the glass and the frame. This is because, on days of intense heat, the glass can expand, and without this space, its expansion could cause the window to break.

Detailed Summary

Relevant Points:

• Superficial Expansion is a Consequence of Linear Expansion: Just like linear expansion, superficial expansion occurs due to the increase in the vibration amplitude of the particles that make up a material when it is heated. Therefore, superficial expansion is a direct effect of linear expansion and shares the same physical law with it.

• Law of Superficial Expansion (Gay-Lussac's Law): The variation in area of a body is directly proportional to its initial area and the temperature variation it is subjected to. This mathematical relationship is fundamental for the understanding and calculation of superficial expansions.

• Coefficient of Superficial Expansion: Each substance has a coefficient of superficial expansion, which indicates how much the substance's area changes for each degree of temperature variation. This coefficient is a constant material property for a range of temperatures, and its value is essential for the application of the Law of Superficial Expansion.

• Practical Applications of Superficial Expansion: Understanding superficial expansion is essential for the design and construction of structures, such as bridges, and for the manipulation of elements, such as glass installation.

Conclusions:

• Expansion is an Inherent Phenomenon of Matter: All bodies, when heated, undergo increases in their dimensions, whether they are length, area, or volume. This is a natural phenomenon and important to be understood for numerous practical and theoretical applications.

• Expansion is Affected by the Material: The expansion coefficient, whether linear, superficial, or volumetric, varies according to the material. This property must be taken into account in situations of design, construction, or material manipulation.

Exercises:

1. Exercise 1: A square has a side measuring 2m and has a superficial expansion coefficient γ = 2.1 x 10^-6 1/°C. What will be the area of the square when the temperature increases from 20°C to 50°C?

2. Exercise 2: A rectangular block of copper has dimensions 15cm x 25cm x 30cm. If the superficial expansion coefficient of copper is γ = 5 x 10^-5 1/°C, what will be the increase in the area of one of its faces when it is heated from 20°C to 100°C?

3. Exercise 3 (Challenge!): A concrete slab has dimensions 4m x 5m x 0.20m. Knowing that the linear expansion coefficient of concrete is α = 11 x 10^-6 1/°C, what will be the volume variation of this slab when it is heated from 25°C to 40°C?