An iron railroad rail is 800 ft long when the temperature is 31°C. What is its length (in ft) when the temperature is - 17°C?

799.54 ft

Explanation:

Linear thermal expansion is:

ΔL = α L₀ ΔT

where ΔL is the change in length,

α is the linear thermal expansion coefficient,

L₀ is the original length,

and ΔT is the change in temperature.

Given:

α = 1.2*10⁻⁵ / °C

L₀ = 800 ft

ΔT = - 17°C - 31°C = - 48°C

Find: ΔL

ΔL = (1.2*10⁻⁵ / °C) (800 ft) (-48°C)

ΔL = - 0.4608

Rounded to two significant figures, the change in length is - 0.46 ft.

Therefore, the final length is approximately 800 ft - 0.46 ft = 799.54 ft.