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?

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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