Question

How much the lengths of various substances change with temperature is given by their coefficients of linear expansion, α. The greater the value of α, the greater the change in length for a given change in temperature. Three kinds of metal wires, (a), (b), and (c), are stretched between distant telephone poles. From greatest to least, rank the wires in how much they’ll sag on a hot summer day:

(a) copper, α=17×10−6/∘C;
(b) aluminum, α=24×10−6/∘C;
(c) steel, α=11×10−6/∘C.

Answer 1

aluminium > copper > steel (amount which get sag)

Step-by-step explanation:

Theory

Linear expansivity (α) : The increase in length, per unit length per degree rise in temperature.

Therefore, α = Δl/Lθ

Δl = increase in length ( amount of sag in this case )

L = length of wire

θ = temperature change

We get, Δl = Lαθ

From that we get, amount of sag ∝ Linear expansivity (α)

Initial length of all three wires are the same.

The temperature change they subject also the same.

So the factor that changes the amount of sag is the coefficient of linear expansivity.