Question 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?

Answer: 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. Log in to Reply

Answer: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.