A steel bridge is 500.0 m long when the temperature is 25.00 OC. What is the length on a cold day when the temperature is minus 20.0 oC? The coefficient of expansion for steel is 12 * 10-6.

499.73 m

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.

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