Copper wire has a resistivity g = 1.7 x 10-8 22-m when at 20°C and it has a temperature coefficient a = 3.9 x 10-3 K-¹. A solid cylinder of copper of length L = 85 cm and diameter D = 1.5 mm has one end held at T1 = 15°C and the other end is held at T2 = 230°C. The temperature increases linearly between the two ends of the cylinder. T₁ dx R= L T₂ Part (a) Consider a thin slice of the copper cylinder of thickness dx that is located a distance x from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables x, L, T₁, and T2. Part (b) Determine the total resistance in milliohms.
Copper wire has a resistivity g = 1.7 x 10-8 22-m when at 20°C and it has a temperature coefficient a = 3.9 x 10-3 K-¹. A solid cylinder of copper of length L = 85 cm and diameter D = 1.5 mm has one end held at T1 = 15°C and the other end is held at T2 = 230°C. The temperature increases linearly between the two ends of the cylinder. T₁ dx R= L T₂ Part (a) Consider a thin slice of the copper cylinder of thickness dx that is located a distance x from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables x, L, T₁, and T2. Part (b) Determine the total resistance in milliohms.
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![Copper wire has a resistivity \( q = 1.7 \times 10^{-8} \, \Omega \cdot \text{m} \) at 20°C and it has a temperature coefficient \( \alpha = 3.9 \times 10^{-3} \, \text{K}^{-1} \). A solid cylinder of copper of length \( L = 85 \, \text{cm} \) and diameter \( D = 1.5 \, \text{mm} \) has one end held at \( T_1 = 15^\circ \text{C} \) and the other end is held at \( T_2 = 230^\circ \text{C} \). The temperature increases linearly between the two ends of the cylinder.
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**Diagram Explanation:**
The diagram shows a horizontal cylinder with length \( L \), with the left end at temperature \( T_1 \) and the right end at temperature \( T_2 \). A thin slice of the cylinder with thickness \( dx \) is highlighted at a distance \( x \) from the left end.
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**Part (a):** Consider a thin slice of the copper cylinder of thickness \( dx \) that is located a distance \( x \) from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables \( x, L, T_1, \) and \( T_2 \).
**Part (b):** Determine the total resistance in milliohms.
\[
R =
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Transcribed Image Text:Copper wire has a resistivity \( q = 1.7 \times 10^{-8} \, \Omega \cdot \text{m} \) at 20°C and it has a temperature coefficient \( \alpha = 3.9 \times 10^{-3} \, \text{K}^{-1} \). A solid cylinder of copper of length \( L = 85 \, \text{cm} \) and diameter \( D = 1.5 \, \text{mm} \) has one end held at \( T_1 = 15^\circ \text{C} \) and the other end is held at \( T_2 = 230^\circ \text{C} \). The temperature increases linearly between the two ends of the cylinder.
---
**Diagram Explanation:**
The diagram shows a horizontal cylinder with length \( L \), with the left end at temperature \( T_1 \) and the right end at temperature \( T_2 \). A thin slice of the cylinder with thickness \( dx \) is highlighted at a distance \( x \) from the left end.
---
**Part (a):** Consider a thin slice of the copper cylinder of thickness \( dx \) that is located a distance \( x \) from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables \( x, L, T_1, \) and \( T_2 \).
**Part (b):** Determine the total resistance in milliohms.
\[
R =
\]
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