Question

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?

Answer 1

`d_r=0.6334\ cm`

Step-by-step explanation:

Given:

• temperature of dry ice,
  `T_d=-78.5^(\circ)C`

• diameter of hole,
  `d_h=0.635\ cm`

• temperature of rivets initially,
  `T_r=20.5^(\circ)C`

• coefficient of linear thermal expansion of aluminium,
  `\alpha=25* 10^(-6)\ ^(\circ)C^(-1)`

Now from the equation of linear thermal expansion:

`\Delta d=d_h.\alpha.\Delta T`

`\Delta d=0.635* 25* 10^(-6)* (20.5-(-78.5))`

`\Delta d=0.00157\ cm`

∴Diameter of rivet at 20.5°C:

`d_r=0.635-0.00157`

`d_r=0.6334\ cm`