10) An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length? Aluminum has a linear expansion coefficient of 25 x 10-6 K-1. A) 17.435 cm B) 0.348 cm C) 17.365 cm D) 0.0348 cm
10) An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length? Aluminum has a linear expansion coefficient of 25 x 10-6 K-1. A) 17.435 cm B) 0.348 cm C) 17.365 cm D) 0.0348 cm
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Problem 10:
**An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length?**
**Given:**
- Aluminum has a linear expansion coefficient of \(25 \times 10^{-6} \, \text{K}^{-1}\).
**Options:**
- **A)** 17.435 cm
- **B)** 0.348 cm
- **C)** 17.365 cm
- **D)** 0.0348 cm
#### Solution:
To find the new length of the aluminum rod after heating, we use the formula for linear expansion:
\[ L_{\text{new}} = L_0 \left( 1 + \alpha \Delta T \right) \]
where:
- \(L_0 = 17.400 \, \text{cm}\) (original length)
- \(\alpha = 25 \times 10^{-6} \, \text{K}^{-1}\) (linear expansion coefficient)
- \(\Delta T = 100^\circ \text{C} - 20^\circ \text{C} = 80 \, \text{K}\) (temperature change)
**Calculation:**
\[ L_{\text{new}} = 17.400 \left( 1 + (25 \times 10^{-6} \times 80) \right) \]
\[ L_{\text{new}} = 17.400 \left( 1 + 0.002 \right) \]
\[ L_{\text{new}} = 17.400 \left( 1.002 \right) \]
\[ L_{\text{new}} = 17.435 \, \text{cm} \]
**Correct Answer:**
- **A)** 17.435 cm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f72c006-9b48-426b-aa7e-60007b6c336c%2F4f2ef7fe-1608-4d1e-9df8-9edc90a9f8c2%2Faiusx3d_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 10:
**An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length?**
**Given:**
- Aluminum has a linear expansion coefficient of \(25 \times 10^{-6} \, \text{K}^{-1}\).
**Options:**
- **A)** 17.435 cm
- **B)** 0.348 cm
- **C)** 17.365 cm
- **D)** 0.0348 cm
#### Solution:
To find the new length of the aluminum rod after heating, we use the formula for linear expansion:
\[ L_{\text{new}} = L_0 \left( 1 + \alpha \Delta T \right) \]
where:
- \(L_0 = 17.400 \, \text{cm}\) (original length)
- \(\alpha = 25 \times 10^{-6} \, \text{K}^{-1}\) (linear expansion coefficient)
- \(\Delta T = 100^\circ \text{C} - 20^\circ \text{C} = 80 \, \text{K}\) (temperature change)
**Calculation:**
\[ L_{\text{new}} = 17.400 \left( 1 + (25 \times 10^{-6} \times 80) \right) \]
\[ L_{\text{new}} = 17.400 \left( 1 + 0.002 \right) \]
\[ L_{\text{new}} = 17.400 \left( 1.002 \right) \]
\[ L_{\text{new}} = 17.435 \, \text{cm} \]
**Correct Answer:**
- **A)** 17.435 cm
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