The main span of San Francisco's Golden Gate Bridge is 1275 m long at its coldest. The bridge is exposed to temperatures ranging from -15°C to 40°C. What is its change in length between these temperatures? Assume that the bridge is made entirely of steel.

Strategy

Use the equation for linear thermal expansion ΔL = αLΔT to calculate the change in length, ΔL. Use the coefficient of linear expansion, a, for steel from Table 13.2, and note that the change in temperature, ΔT, is 55°C.

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Solids Aluminum Brass Copper Gold Iron or Steel Invar (Nickel-iron alloy) Lead Silver Glass (ordinary) Glass (Pyrex®) Material Quartz Concrete, Brick Marble (average) Coefficient of linear expansion a(1/°C) 25 x 10-6 19 x 10-6 17 x 10-6 14 x 10-6 12 x 10-6 0.9 x 10-6 29 × 10-6 18 x 10-6 9x10-6 3 x 10-6 0.4 x 10-6 -12 x 10-6 7x10-6 Coefficient of volume expansion B(1/°C) 75 x 10-6 56 x 10-6 51 x 10-6 42 x 10-6 35 x 10-6 2.7 x 10-6 87 x 10-6 54 x 10-6 27 x 10-6 9x10-6 1 x 10-6 -36 x 10-6 2.1 x 10-5