Aluminum rivets used in airplane construction are made...

Aluminum rivets used in airplane construction are made slightly larger than the rivet holes and cooled by "dry ice" (solid $\mathrm{CO}_{2} )$ before being driven. If the diameter of a hole is 4.500 $\mathrm{mm}$ , what should be the diameter of a rivet at $23.0^{\circ} \mathrm{C}$ , if its diameter is to equal that of the hole when the rivet is cooled to $-78.0^{\circ} \mathrm{C}$ , the temperature of dry ice? Assume that the expansion coefficient remains constant at the value given in Table $17.1 .$

Aluminum rivets used in airplane construction are made slightly larger than the rivet holes and cooled
by "dry ice" (solid $\mathrm{CO}_{2} )$ before being driven. If the diameter of a hole is 4.500 $\mathrm{mm}$ , what should be the diameter of a rivet at $23.0^{\circ} \mathrm{C}$ , if its diameter is to equal that of the hole when the rivet is cooled to $-78.0^{\circ} \mathrm{C}$ , the temperature of dry ice? Assume that the expansion coefficient remains constant at the value given in Table $17.1 .$

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Key Concepts

Linear Thermal Expansion

This concept explains how the dimensions of a solid object change with temperature. In particular, the change in length (or any linear dimension like diameter) is directly proportional to the original dimension, the temperature change, and the material's coefficient of expansion. It is expressed as ?L = ?L??T, where ? is the linear expansion coefficient, L? is the original dimension, and ?T is the temperature change.

Coefficient of Linear Expansion

The coefficient of linear expansion is a material-specific constant that quantifies the degree to which a material expands or contracts per unit change in temperature. It is essential for calculating the dimensional changes in objects due to thermal effects, especially when precise fits, like those in mechanical assemblies, are required.

Temperature Differential

This concept pertains to the difference between the initial and final temperatures of a material. The temperature differential determines the magnitude of expansion or contraction when combined with the linear thermal expansion equation, ensuring accurate predictions of dimensional changes when the material is heated or cooled.

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