Copper wire has a resistivity ρ =1.7 x 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 = 55 cm and diameter D = 2.5 mm has one end held at T1 = 0℃ and the other end is held at T2 =220 ℃. The temperature increases linearly between the two ends of the cylinder.
Part (a) Consider a thin slice of the copper cylinder of thickness dr 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 ρ =1.7 x 10-8 Ω·m when at 20°C and it has a temperature coefficient α = 3.9×10-3 K-1.
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 = 2.5 mm has one end held at T1 = 7°C and the other end is held at T2 = 210°C. The temperature increases linearly between the two ends of the cylinder. Given that T= T1 + ( x/L )...
Resistance in metals increases with increasing temperature according to the equation, ρ(T) = ρo(1 + α(T - To)) where α is the temperature coefficient of resistivity and ρo is the resistivity at temperature To. For a particular wire α = 1.5 × 10-3 1/°C and the resistivity is ρo = 8.5 × 10-7 Ω⋅m at To = 125 °C.
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