Question

A metal rod is 0.600 m in length at a temperature of 15.0∘C. When you raise its temperature to 37.0∘C, its length increases by 0.280 mm. What is the coefficient of linear expansion of the metal?

Answer 1

The coefficient of linear expansion of the metal is ∝ = 2.91 x 10⁻⁵ °C⁻¹.

Step-by-step explanation:

We know that Linear thermal expansion is represented by the following equation

Δ L = L x ∝ x Δ T ---- (1)

where Δ L is the change in length, L is for length, ∝ is the coefficient of linear expression and Δ T is the change in temperature.

Given that:

L = 0.6 m

T₁ = 15° C

T₂ = 37° C

Δ L = 0.28 mm

∝ = ?

Solution:

We know that Δ T = T₂ ₋ T₁

Putting the values of T₁ and T₂ in above equation, we get

Δ T = 37 - 15

Δ T = 22 °C

Also Δ L = 0.28 mm

Converting the mm to m

Δ L = 0.00028 m

Putting the values of Δ T, Δ L, L in equation 1, we get

0.00028 = 0.6 x ∝ x 22

Rearranging the equation, we get

∝ = 0.00028 / (0.6 x 16)

∝ = 0.00028 / 13.2

∝ = 2.12 x 10⁻⁵ °C⁻¹