The dependence of thermal expansion on temperature, substance, and length is determined by the equation
ΔL = αLΔT where ΔL is the change in diameter L of rod, ΔT is the change in temperature, and α is the coefficient of linear expansion.
We have
L=2mm=2⋅10−3m
ΔL=1.995mm−2mm=−0.005mm=−5⋅10−6m The coefficient of linear expansion for iron at 20oC is (https://en.wikipedia.org/wiki/Thermal_expansion)
α=11.8⋅10−6K−1=11.8⋅10−6∘C−1 Substituting the known values into the formula, we get
−5⋅10−6m = 11.8⋅10−6∘C−1⋅2⋅10−3m⋅ΔT Hence the change in temperature is
ΔT=−11.8⋅25⋅103∘C=−212∘C So the machinist would have to cool the iron rod to make it fit the hole by 212 °C
Comments