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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

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter16: Temperature And The Kinetic Theory Of Gases
Section: Chapter Questions
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Please show all calculations and type them out So that I will be able to read them and understand what you're saying I have bad eyesight and it is very difficult for me to read handwriting 

### 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
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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