Answer:
The increase in length of a material due to temperature change is given by the formula:
ΔL = αLΔT
where:
ΔL is the change in length
α is the coefficient of linear thermal expansion of the material
L is the original length of the material
ΔT is the change in temperature
In this case, the rod has an original length of L = 20.0 m and a coefficient of linear thermal expansion of α = 4.0 × 10^-5 K^-1. The temperature change is ΔT = 80°C - 25°C = 55°C.
Plugging these values into the formula, we get:
ΔL = αLΔT
ΔL = (4.0 × 10^-5 K^-1)(20.0 m)(55°C)
ΔL = 0.044 m
Therefore, the increase in length of the rod is 0.044 m or 4.4 cm.