Dilatacion Superficial Ejercicios Resueltos (480p 2024)

Problem:
A square hole in a metal sheet expands when heated. Does the hole area increase or decrease? Prove.

Solution:
The hole behaves as if made of the same material.
If you imagine the missing part, its boundaries expand outward exactly as solid material would.
So hole area increases by (\Delta A = A_hole,0 \cdot \beta \cdot \Delta T).

Answer: Increases, same (\beta) as the plate.

La fórmula que rige la dilatación superficial es análoga a la dilatación lineal, pero considera la variación del área total.

La ecuación fundamental es:

$$A_f = A_0 [1 + \beta \cdot \Delta T]$$

Donde:

Problem: A copper plate has an area of (0.5 , \textm^2) at (20 , \text°C). The coefficient of linear expansion of copper is (\alpha = 1.7 \times 10^-5 , \text°C^-1). Calculate: a) The coefficient of surface expansion. b) The increase in area when heated to (180 , \text°C). c) The final area.

Solution:

(a) Coefficient of surface expansion
(\beta = 2\alpha = 2(1.7 \times 10^-5) = 3.4 \times 10^-5 , \text°C^-1)

(b) Temperature change
(\Delta T = 180 - 20 = 160 , \text°C)

(c) Area increase
(\Delta A = \beta A_0 \Delta T)
(\Delta A = (3.4 \times 10^-5)(0.5)(160))
(\Delta A = (3.4 \times 10^-5) \times 80)
(\Delta A = 2.72 \times 10^-3 , \textm^2) dilatacion superficial ejercicios resueltos

(d) Final area
(A_f = A_0 + \Delta A = 0.5 + 0.00272 = 0.50272 , \textm^2)

Answer: (\beta = 3.4 \times 10^-5 , \text°C^-1), (\Delta A = 0.00272 , \textm^2), (A_f = 0.50272 , \textm^2).

Enunciado: Una ventana de vidrio (α=9×10⁻⁶) tiene 1.5 m² a 22 °C. ¿Qué área tendrá a –18 °C (temperatura invernal)?

Solución:

Respuesta: 1.4989 m². La contracción es pequeña pero significativa para sellos herméticos.

This guide provides a complete foundation for understanding and solving surface expansion problems. Practice with different materials and temperature ranges to master the topic.

The following resources and solved exercises will help you master superficial expansion (dilatación superficial), which occurs when a solid's surface area increases due to a rise in temperature. Essential Study Papers and PDF Guides

These documents contain detailed theory and step-by-step problem sets:

Apuntes y ejercicios resueltos de DILATACION SUPERFICIAL: A comprehensive study document on Docsity specifically focused on notes and solved problems.

GUÍA 4 FÍSICA - Dilatación Superficial: This guide includes the fundamental formula

and provides clear examples, such as calculating the final area of a glass window when heated from 21∘C21 raised to the composed with power C 35∘C35 raised to the composed with power C Problem: A square hole in a metal sheet

Ejemplos y ejercicios de dilatación superficial: Available on Scribd, this paper describes common problems involving steel bars and aluminum plates.

Física II: Guía de Problemas: A PDF problem set covering various types of thermal expansion, including cross-sectional changes in steel. Solved Example Step-by-Step Problem: A glass window has an initial area ( A0cap A sub 0 21∘C21 raised to the composed with power C . What is its final area ( Afcap A sub f ) if the temperature rises to 35∘C35 raised to the composed with power C Identify the variables: (coefficient of superficial expansion) for glass (value varies by glass type). Apply the formula:

Af=A0⋅(1+γ⋅ΔT)cap A sub f equals cap A sub 0 center dot open paren 1 plus gamma center dot cap delta cap T close paren Calculate the change: Multiply the coefficient by the temperature change. Add 1 to that result. Multiply by the original area to find the new surface area. Key Formulas to Remember

For a comprehensive guide on superficial expansion (dilatación superficial), you can refer to the following educational materials and solved exercises. These resources provide clear definitions, formulas, and step-by-step solutions for physics students. Key Educational Resources Comprehensive PDF Guide Physics Guide from Educajovenes y Adultos

includes the conceptualization of superficial expansion, a table of expansion coefficients, and a solved problem regarding a glass window at varying temperatures. Solved Exercise Collections Studocu - Ejercicios Resueltos

: Provides detailed step-by-step solutions for problems involving iron gates and temperature decreases. Scribd - Practical Physics Class

: Offers practical examples such as calculating the expansion of a steel sheet and explains the relationship between linear and superficial coefficients ( Fundamental Formula To solve these exercises, the primary formula used is:

cap delta cap A equals cap A sub 0 center dot gamma center dot cap delta cap T cap delta cap A : Variation in area. cap A sub 0 : Initial area.

: Coefficient of superficial expansion (typically twice the linear coefficient, cap delta cap T : Variation in temperature ( Subsistema de Preparatoria Abierta del Estado de Puebla Step-by-Step Example

If you are starting a problem, following this algorithm from Liceo Corregidora is helpful: Identify Data : Note the initial area ( cap A sub 0 ), initial temperature ( cap T sub i ), final temperature ( cap T sub f ), and the material's coefficient. Determine the Goal : Identify if you need the area change ( cap delta cap A ) or the final area ( cap A sub f Substitution and Calculation

: Plug values into the formula, ensuring temperature units match the coefficient (usually Celsius or Kelvin). Liceo corregidora solved example for a particular material, like aluminum or steel? La fórmula que rige la dilatación superficial es

The result for a solved exercise on superficial expansion (dilatación superficial) typically involves calculating the change in area of an object when subjected to a temperature change. The Formula The fundamental equation used in these exercises is:

ΔA=A0⋅β⋅ΔTcap delta cap A equals cap A sub 0 center dot beta center dot cap delta cap T ΔAcap delta cap A is the change in area ( A0cap A sub 0 is the initial area. is the coefficient of superficial expansion (usually is the linear expansion coefficient). ΔTcap delta cap T is the change in temperature ( Step 1: Calculate the Area Change

In a common problem, such as a metal plate heating up, you first identify the known values ( A0cap A sub 0 Ticap T sub i Tfcap T sub f , and the material's ). For example, if you have a steel plate ( ), you calculate by doubling Step 2: Find the Final Area Once you have ΔAcap delta cap A , you find the final area ( Afcap A sub f

Af=A0+ΔAorAf=A0(1+βΔT)cap A sub f equals cap A sub 0 plus cap delta cap A space or space cap A sub f equals cap A sub 0 open paren 1 plus beta cap delta cap T close paren Solved Example Summary 2m22 m squared copper plate ( ) is heated from Identify ΔTcap delta cap T : Apply Formula: Result: The new area is 2.0034m22.0034 m squared

For a detailed walkthrough on solving for final temperature or area in superficial expansion:

To see how superficial expansion compares to linear and volumetric problems: