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Aluminum rivets used in airplane construction are made slightly too large for the rivet boles to be sure of a tight fit. The rivets are cooled with dry ice (−78.5∘C) before they are driven into the holes. if the holes have a diameter of 0.6350 cm at
20.5∘C , what should be the diameter of the rivers at 20.5∘C if they are to just fit when cooled to the temperature of dry ice?

Respuesta :

Answer:

[tex]d_r=0.6334\ cm[/tex]

Explanation:

Given:

  • temperature of dry ice, [tex]T_d=-78.5^{\circ}C[/tex]
  • diameter of hole, [tex]d_h=0.635\ cm[/tex]
  • temperature of rivets initially, [tex]T_r=20.5^{\circ}C[/tex]
  • coefficient of linear thermal expansion of aluminium, [tex]\alpha=25\times 10^{-6}\ ^{\circ}C^{-1}[/tex]

Now from the equation of linear thermal expansion:

[tex]\Delta d=d_h.\alpha.\Delta T[/tex]

[tex]\Delta d=0.635\times 25\times 10^{-6}\times (20.5-(-78.5))[/tex]

[tex]\Delta d=0.00157\ cm[/tex]

∴Diameter of rivet at 20.5°C:

[tex]d_r=0.635-0.00157[/tex]

[tex]d_r=0.6334\ cm[/tex]

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