Question

The temperature coefficient of resistance α in equation R(T)=R0[1+α(T−T0)] equals the temperature coefficient of resistivity α in equation ρ(T)=ρ0[1+α(T−T0)] only if the coefficient of thermal expansion is small. A cylindrical column of mercury is in a vertical glass tube. At 20 ∘C, the length of the mercury column is 12.0 cm. The diameter of the mercury column is 1.6 mm and doesn't change with temperature because glass has a small coefficient of thermal expansion. The coefficient of volume expansion of the mercury is 18⋅10−5K−1, its resistivity at 20 ∘C is 95⋅10−8Ω⋅m, and its temperature coefficient of resistivity is 0.00088 (∘C)−1.

Part A: At 20 ∘C, what is the resistance between the ends of the mercury column?

Express your answer using two significant figures.

Part B

The mercury column is heated to 60 ∘C. What is the change in its resistivity?

Express your answer using two significant figures.

Part C

What is the change in its length?

Express your answer using two significant figures.

Part D

Explain why the coefficient of volume expansion, rather than the coefficient of linear expansion, determines the change in length.

Answer 1

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