Materials expand when heated. Consider a metal rod of length L0 at temperature T0. If the temperature is changed by an amount Δ T , then the rod's length changes by ΔL = αL0ΔT , where α is the thermal expansion coefficient. 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.