The relationship Lf = Li (1 + T) is an approximation that works when the average coefficient of expansion is small. If is large, one

The relationship Lf = Li (1 + αΔT) is an approximation that works when the average coefficient of expansion is small. If α is large, one must integrate the relationship dL/dT =αL to determine the final length. (a) Assuming that the coefficient of linear expansion is constant as L varies, determine a general expression for the final length. (b) Given a rod of length 1.00 m and a temperature change of 100.0°C, determine the error caused by the approximation when α = 2.00 X 10-5 (°C)-1 (a typical value for a metal) and when & = 0.020 0 (°C)-1 (an unrealistically large value for comparison).