Materials expand when heated. Consider a metal rod of length L₀ at temperature T₀. If the temperature is changed by an amount ΔT, then the rod’s length approximately changes by ΔL = αL₀ΔT, where α is the thermal expansion coefficient and ΔT is not an extreme temperature change. For steel, α = 1.24 × 10⁻⁵ °C⁻¹.
(a) A steel rod has length L₀ = 40 cm at T₀ = 40°C. Find its length at T = 90°C.
(b) Find its length at T = 50°C if its length at T₀ = 100°C is 65 cm.
(c) Express length L as a function of T if L₀ = 65 cm at T₀ = 100°C.