11) A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods are at an initial temperature of 0° C. The rods are placed in line with a gap of 1.2 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature of both rods is raised equally until they are barely in contact. At what temperature does contact occur? The coefficients of linear expansion of brass and aluminum are 2.0 x10-5 K-1 (brass) and 2.4 x 10-5 K-1 (aluminum). -120.0 cm- aluminum B) 420°C C) 510°C D) 470°C E) 440°C brass A) 490°C
11) A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods are at an initial temperature of 0° C. The rods are placed in line with a gap of 1.2 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature of both rods is raised equally until they are barely in contact. At what temperature does contact occur? The coefficients of linear expansion of brass and aluminum are 2.0 x10-5 K-1 (brass) and 2.4 x 10-5 K-1 (aluminum). -120.0 cm- aluminum B) 420°C C) 510°C D) 470°C E) 440°C brass A) 490°C
College Physics
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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![### Linear Expansion of Metal Rods
**Problem Statement:**
Given:
- A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long, both at an initial temperature of 0°C.
- The rods are placed end to end with a gap of 1.2 cm between them.
- The distance between the far ends of the rods is maintained at 120.0 cm throughout.
- The temperature of both rods is raised equally until they are barely in contact.
**Objective:**
Determine the temperature at which both rods are barely in contact.
**Coefficients of Linear Expansion:**
- Brass: \(2.0 \times 10^{-5} \, \text{K}^{-1}\)
- Aluminum: \(2.4 \times 10^{-5} \, \text{K}^{-1}\)
**Diagram Explanation:**
- The diagram displays the brass and aluminum rods aligned with a gap of 1.2 cm between them.
- The combined length of the rods plus the gap is 120.0 cm.
**Solution:**
To find the temperature at which both rods will be in contact, we need to calculate the linear expansion of each rod as the temperature increases. The formula for linear expansion is:
\[ \Delta L = L_0 \alpha \Delta T \]
Where:
- \(\Delta L\) = Change in length
- \(L_0\) = Original length
- \(\alpha\) = Coefficient of linear expansion
- \(\Delta T\) = Change in temperature
For brass:
\[ \Delta L_{brass} = 69.5 \, \text{cm} \times 2.0 \times 10^{-5} \, \text{K}^{-1} \times \Delta T \]
For aluminum:
\[ \Delta L_{aluminum} = 49.3 \, \text{cm} \times 2.4 \times 10^{-5} \, \text{K}^{-1} \times \Delta T \]
The total expansion should equal the gap for the rods to barely touch:
\[ \Delta L_{brass} + \Delta L_{aluminum} = 1.2 \, \text{cm} \]
Substitute \(\Delta L\) values:
\[ (69.5 \times 2.0 \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6527be19-4214-4a2f-aca2-4f82253fbdd1%2F589a2d68-6123-48c6-9a2e-1ddbbadbadf6%2Fj3eezl2_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear Expansion of Metal Rods
**Problem Statement:**
Given:
- A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long, both at an initial temperature of 0°C.
- The rods are placed end to end with a gap of 1.2 cm between them.
- The distance between the far ends of the rods is maintained at 120.0 cm throughout.
- The temperature of both rods is raised equally until they are barely in contact.
**Objective:**
Determine the temperature at which both rods are barely in contact.
**Coefficients of Linear Expansion:**
- Brass: \(2.0 \times 10^{-5} \, \text{K}^{-1}\)
- Aluminum: \(2.4 \times 10^{-5} \, \text{K}^{-1}\)
**Diagram Explanation:**
- The diagram displays the brass and aluminum rods aligned with a gap of 1.2 cm between them.
- The combined length of the rods plus the gap is 120.0 cm.
**Solution:**
To find the temperature at which both rods will be in contact, we need to calculate the linear expansion of each rod as the temperature increases. The formula for linear expansion is:
\[ \Delta L = L_0 \alpha \Delta T \]
Where:
- \(\Delta L\) = Change in length
- \(L_0\) = Original length
- \(\alpha\) = Coefficient of linear expansion
- \(\Delta T\) = Change in temperature
For brass:
\[ \Delta L_{brass} = 69.5 \, \text{cm} \times 2.0 \times 10^{-5} \, \text{K}^{-1} \times \Delta T \]
For aluminum:
\[ \Delta L_{aluminum} = 49.3 \, \text{cm} \times 2.4 \times 10^{-5} \, \text{K}^{-1} \times \Delta T \]
The total expansion should equal the gap for the rods to barely touch:
\[ \Delta L_{brass} + \Delta L_{aluminum} = 1.2 \, \text{cm} \]
Substitute \(\Delta L\) values:
\[ (69.5 \times 2.0 \times
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