Copper wire has a resistivity ρ = 1.7 × 10-8 Ω⋅m when at 20°C and it has a temperature coefficient α = 3.9 × 10-3 K-1. A solid cylinder of copper of length L = 85 cm and diameter D = 3.5 mm has one end held at T1 = 14°C and the other end is held at T2 = 210°C. The temperature increases linearly between the two ends of the cylinder. 1A) 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. The answer to part a is T=( x/L ) T2 + ( 1 - ( x/L ) ) T1 b) Determine the total resistance in milliohms.
Ohm's law
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Copper wire has a resistivity ρ = 1.7 × 10-8 Ω⋅m when at 20°C and it has a temperature coefficient α = 3.9 × 10-3 K-1. A solid cylinder of copper of length L = 85 cm and diameter D = 3.5 mm has one end held at T1 = 14°C and the other end is held at T2 = 210°C. The temperature increases linearly between the two ends of the cylinder.
1A) 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.
The answer to part a is
| T=( x/L ) T2 + ( 1 - ( x/L ) ) T1 |
b)
| Determine the total resistance in milliohms. | |
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