What is the coefficient of thermal expansion used to calculate length change for galvanized steel in the given example?

What is the coefficient of thermal expansion used to calculate length change for galvanized steel in the given example?

• A. 0.0000067
• B. 0.000067
• C. 0.00000067
• D. 0.000667

Answer: (A)

The key idea is that the coefficient of linear thermal expansion tells you how much length changes per unit length for every degree of temperature change. For galvanized steel in this example, the value used is 0.0000067, or 6.7 × 10^-6. This means a one-inch length grows by about 0.0000067 inches for each 1 °F (or 1 °C, depending on the unit) of temperature rise. Use ΔL = α × L × ΔT to find the total length change. For a 240-inch length with a 40 °F temperature increase, the change would be roughly 0.0000067 × 240 × 40 ≈ 0.064 inches. The other options would predict changes that are tenfold, hundredfold, or more off, so they don’t fit the example. The galvanizing coating doesn’t materially change α, so galvanized steel uses the same order of magnitude for calculation.

The key idea is that the coefficient of linear thermal expansion tells you how much length changes per unit length for every degree of temperature change. For galvanized steel in this example, the value used is 0.0000067, or 6.7 × 10^-6. This means a one-inch length grows by about 0.0000067 inches for each 1 °F (or 1 °C, depending on the unit) of temperature rise. Use ΔL = α × L × ΔT to find the total length change. For a 240-inch length with a 40 °F temperature increase, the change would be roughly 0.0000067 × 240 × 40 ≈ 0.064 inches. The other options would predict changes that are tenfold, hundredfold, or more off, so they don’t fit the example. The galvanizing coating doesn’t materially change α, so galvanized steel uses the same order of magnitude for calculation.