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?

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?

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Sigridomena 3 years 2021-09-02T08:08:10+00:00 1 Answers 1 views 0

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    2021-09-02T08:09:32+00:00

    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.

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