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