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9 July, 09:04

A hole in a copper plate has a diameter of 1.325 cm at 21.00 degrees Celsius. What is the diameter of the hole at 248.0 degrees Celsius?

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  1. 9 July, 09:12
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    The diameter of the hole at 248.0 degrees Celsius is 1.330 cm.

    Explanation:

    given information

    diameter, d₀ = 1.325 cm

    initial temperature, T₁ = 21°

    final temperature, T₂ = 248.0°

    to calculate the diameter after the temperature increased

    Δd = α d₀ ΔT

    where

    Δd = the change of diameter

    α = thermal expansion constant

    d₀ = initial diameter

    ΔT = the change of temperature

    thermal expansion constant for copper is 17 x 10⁻⁶/°C

    thus,

    Δd = α d₀ ΔT

    = (17 x 10⁻⁶) (1.325) (248 - 21)

    = 0.005 cm

    so, the diameter of the hole at 248°C is

    Δd = d - d₀

    d = Δd + d₀

    = 0.005 + 1.325

    = 1.330 cm
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