### Thermal Expansion Concept**Problem Statement:**At 20.0 °C, an aluminum sleeve with an inside diameter of 5.000 cm just fits over a steel rod with an outside diameter of 5.000 cm. Determine the size of the gap in centimeters between the sleeve and the rod when they are both at 100.0 °C.**Given:**- Coefficient of linear expansion for steel, \( \alpha_{\text{st}} = 11.0 \times 10^{-6} \, \text{C}^{-1} \)- Coefficient of linear expansion for aluminum, \( \alpha_{\text{al}} = 23.0 \times 10^{-6} \, \text{C}^{-1} \)**Diagrams:**1. **Diagram at 20.0 °C:** - A cross-sectional view showing the aluminum sleeve fitting exactly over the steel rod, both with diameters of 5.000 cm.2. **Diagram at 100.0 °C:** - A cross-sectional view showing a gap between the aluminum sleeve and the steel rod due to differential thermal expansion.**Explanation:**- As both materials are heated from 20.0 °C to 100.0 °C, they expand, but at different rates due to differing coefficients of thermal expansion.- The aluminum sleeve expands more than the steel rod, creating a gap.**Objective:**Calculate the size of the gap formed at 100.0 °C based on the thermal expansion properties of aluminum and steel.

Answered: Image /qna-images/answer/ec7ff19d-0688-46f7-be70-5c1f2cf704d3.jpg

TE-1 At 20.0 °C an aluminum sleeve with an inside diameter of 5.000 cm just fits over a steel rod with an outside diameter of 5.000 cm as shown below. Find the size of the gap in centimeters between the sleeve and the rod when they are both at 100.0 °C. At 20.0°C At 100.0°C 11.0x10 23.0x10 steel Use a = and a %3D C° 5.000cm gap aluminum rch

TE-1 At 20.0 °C an aluminum sleeve with an inside diameter of 5.000 cm just fits over a steel rod with an outside diameter of 5.000 cm as shown below. Find the size of the gap in centimeters between the sleeve and the rod when they are both at 100.0 °C. At 20.0°C At 100.0°C 11.0x10 23.0x10 steel Use a = and a %3D C° 5.000cm gap aluminum rch

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter18: Temperature

Section: Chapter Questions

Problem 1P

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### Thermal Expansion Concept

**Problem Statement:**

At 20.0 °C, an aluminum sleeve with an inside diameter of 5.000 cm just fits over a steel rod with an outside diameter of 5.000 cm. Determine the size of the gap in centimeters between the sleeve and the rod when they are both at 100.0 °C.

**Given:**

- Coefficient of linear expansion for steel, \( \alpha_{\text{st}} = 11.0 \times 10^{-6} \, \text{C}^{-1} \)
- Coefficient of linear expansion for aluminum, \( \alpha_{\text{al}} = 23.0 \times 10^{-6} \, \text{C}^{-1} \)

**Diagrams:**

1. **Diagram at 20.0 °C:**
- A cross-sectional view showing the aluminum sleeve fitting exactly over the steel rod, both with diameters of 5.000 cm.

2. **Diagram at 100.0 °C:**
- A cross-sectional view showing a gap between the aluminum sleeve and the steel rod due to differential thermal expansion.

**Explanation:**

- As both materials are heated from 20.0 °C to 100.0 °C, they expand, but at different rates due to differing coefficients of thermal expansion.
- The aluminum sleeve expands more than the steel rod, creating a gap.

**Objective:**

Calculate the size of the gap formed at 100.0 °C based on the thermal expansion properties of aluminum and steel.

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