Question

Aluminum rivets used in airplane construction are made slightly larger than the rivet holes and cooled by "dry ice" (solid CO₂) before being driven. If the diameter of a hole is 4.460 mm , what should be the diameter of a rivet at 23.0 ˚ ∘C, if its diameter is to equal that of the hole when the rivet is cooled to -79.5 ˚ C, the temperature of dry ice? Assume that the expansion coefficient of aluminum is 2.4×10⁻⁵(˚ C)−1 and remains constant.

Answer 1

To determine the diameter of an aluminum rivet at 23.0°C that will fit into a 4.460 mm hole when cooled to -79.5°C, apply the linear expansion formula using the known values and the coefficient of expansion for aluminum.

Step-by-step explanation:

The question is asking about thermal expansion in the context of fitting aluminum rivets into holes in airplane construction. Aluminum expands when heated and contracts when cooled, and the size of the rivets is adjusted based on their temperatures to fit perfectly into the holes. To find the needed diameter of a rivet at 23.0°C so that it will fit into a hole of diameter 4.460 mm when cooled to -79.5°C, we use the linear expansion formula:

×(Original Diameter) = Final Diameter / (1 + ×(Temperature Change))

Plugging in the values:

×(4.460 mm) = Rivet Diameter at 23°C / (1 + (2.4×10⁵°C⁻¹)(23.0°C - (-79.5°C)))

Solve for Rivet Diameter at 23°C.