Answer:
499.73 m
Step-by-step explanation:
We'll begin by calculating the change in the temperature. This can be obtained as follow:
Initial temperature (T₁) = 25 °C
Final temperature (T₂) = –20° C
Change in temperature (ΔT) =?
ΔT = T₂ – T₁
ΔT = –20 – 25
ΔT = –45 °C
Finally, we shall determine the length on a cold day at –20° C. This can be obtained as follow:
Length at 25°C (L₁) = 500 m
Coefficient of linear expansion (α) = 12×10¯⁶ /°C
Change in temperature (ΔT) = –45 °C
Length at –20 °C (L₂) =?
α = L₂ – L₁ / L₁ΔT
12×10¯⁶ = L₂ – 500 / (500 × –45)
12×10¯⁶ = L₂ – 500 / –22500
Cross multiply
L₂ – 500 = 12×10¯⁶ × –22500
L₂ – 500 = –0.27
Collect like terms
L₂ = –0.27 + 500
L₂ = 499.73 m
Therefore, the length on a cold day at –20° C is 499.73 m.