The change in length of a material due to temperature change is given by:
ΔL = αLΔT
where ΔL is the change in length, α is the coefficient of linear expansion, L is the initial length, and ΔT is the change in temperature.
The coefficient of linear expansion for steel is 1.2 x 10^-5 K^-1, and for copper is 1.7 x 10^-5 K^-1.
The change in temperature is:
ΔT = 41.0 - (-12.0) = 53.0 °C
The change in length for the steel bar is:
ΔL_steel = α_steel * L * ΔT = 1.2 x 10^-5 * 1.500 * 53.0 = 0.001914 m
The change in length for the copper bar is:
ΔL_copper = α_copper * L * ΔT = 1.7 x 10^-5 * 1.500 * 53.0 = 0.002565 m
Therefore, the difference in the lengths of the two bars at 41.0 °C is:
ΔL_copper - ΔL_steel = 0.002565 - 0.001914 = 0.000651 m.
,