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I see you've uploaded an image with a set of physics and mathematics questions related to thermal expansion. Let me extract and solve each of these questions for you:

### 1. **Un alambre de cobre mide 5 m a la temperatura de 10°C. ¿Cuánto medirá a 60°C, si el coeficiente de dilatación lineal es \(1.7 \times 10^{-5} \, ^\circ \text{C}^{-1}\)?**

The formula for linear expansion is:
\[
\Delta L = L_0 \cdot \alpha \cdot \Delta T
\]
where:
- \( L_0 = 5 \, \text{m} \) is the original length,
- \( \alpha = 1.7 \times 10^{-5} \, ^\circ \text{C}^{-1} \) is the coefficient of linear expansion,
- \( \Delta T = 60^\circ \text{C} - 10^\circ \text{C} = 50^\circ \text{C} \) is the temperature change.

Let me calculate this.

### 2. **Un alambre de aluminio mide 20 m a la temperatura de 20°C. ¿Cuánto mide a 70°C, si el coeficiente de dilatación lineal es \(2.4 \times 10^{-5} \, ^\circ \text{C}^{-1}\)?**

We apply the same formula:
\[
\Delta L = L_0 \cdot \alpha \cdot \Delta T
\]
where:
- \( L_0 = 20 \, \text{m} \),
- \( \alpha = 2.4 \times 10^{-5} \, ^\circ \text{C}^{-1} \),
- \( \Delta T = 70^\circ \text{C} - 20^\circ \text{C} = 50^\circ \text{C} \).

Let me compute this as well.

### 3. **Un alambre de acero de 40 cm al incorporarse a una temperatura de 80°C alcanza los 60 cm. ¿Cuál es el coeficiente de dilatación de este alambre para ese rango de 80 cm?**

We can rearrange the linear expansion formula to find \( \alpha \):
\[
\alpha = \frac{\Delta L}{L_0 \cdot \Delta T}
\]
Given that:
- \( L_0 = 40 \, \text{cm} \),
- \( L = 60 \, \text{cm} \),
- \( \Delta T = 80^\circ \text{C} \),
\[
\Delta L = 60 \, \text{cm} - 40 \, \text{cm} = 20 \, \text{cm}
\]

I will solve this next.

### 4. **Un alambre de un metal sin nombre mide 1 m. ¿Cuál es su coeficiente de dilatación lineal si a 100°C se alarga 3 mm?**

Again, we use the linear expansion formula:
\[
\alpha = \frac{\Delta L}{L_0 \cdot \Delta T}
\]
Given:
- \( L_0 = 1 \, \text{m} = 1000 \, \text{mm} \),
- \( \Delta L = 3 \, \text{mm} \),
- \( \Delta T = 100^\circ \text{C} \).

This can be calculated similarly.

### 5. **¿Qué es el área "A" y "B"?**

This might require clarification from the image, as I don't see enough context to answer.

### 6. **Se quiere que la tira en la pared sea de 3 m de largo. ¿Cuál será la longitud a la máxima temperatura esperada?**

This is a thermal expansion problem, where I can use the linear expansion formula if given the coefficient of expansion.

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Let me start by calculating the first few problems. I will return with the results!Here are the results for the first four problems:

1. **Copper wire (initial length 5 m, temperature change from 10°C to 60°C):**  
   The final length of the copper wire will be **5.00425 meters**.

2. **Aluminum wire (initial length 20 m, temperature change from 20°C to 70°C):**  
   The final length of the aluminum wire will be **20.024 meters**.

3. **Steel wire (initial length 40 cm, expands to 60 cm at 80°C):**  
   The coefficient of linear expansion for the steel wire is **\( \alpha = 6.25 \times 10^{-3} \, ^\circ \text{C}^{-1} \)**.

4. **Unknown metal (initial length 1 m, expands by 3 mm at 100°C):**  
   The coefficient of linear expansion for this metal is **\( \alpha = 3.0 \times 10^{-5} \, ^\circ \text{C}^{-1} \)**.

Would you like further details or explanations on any of these? Let me know!

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Here are 5 related questions to deepen your understanding:
1. How does the expansion of solids differ between different materials?
2. What happens to the expansion coefficient at extremely high or low temperatures?
3. Why does the length change linearly with temperature in the cases above?
4. How does thermal expansion affect the design of bridges or railways?
5. What are the limitations of using the linear expansion formula for large temperature changes?

**Tip:** When dealing with very large or small expansions, always check if the coefficient of expansion remains constant across the temperature range!

Un alambre de cobre mide 5 m a la temperatura de 10°C. ¿Cuánto medirá a 60°C, si el coeficiente de dilatación lineal es 1.7 × 10⁻⁵ °C⁻¹?

Learn how to solve a linear thermal expansion problem involving a copper wire with an initial length of 5 meters at 10°C. This solution uses the formula ΔL = L₀ * α * ΔT, focusing on how temperature changes affect material length.

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