How does thermal expansion affect a parts fit, and what is the formula for linear expansion?

• A. It can increase or decrease clearance; deltaL = alpha * deltaT.
• B. Delta L should be computed as deltaL = alpha * L0 * deltaT.
• C. Delta L equals alpha times deltaT.
• D. Delta L equals alpha times L0 plus deltaT.

Answer: (B)

Thermal expansion changes a part’s length when temperature changes. The amount it expands or contracts depends on three things: the original length, the material’s coefficient of linear expansion, and how big the temperature change is. The correct expression is deltaL = alpha * L0 * deltaT because it multiplies the coefficient by the original length to scale the change in length. Here, alpha tells you how much length changes per degree per unit length, L0 is where you start, and deltaT is how much the temperature shifts.

This matters for fits because a part that’s a snug clearance at one temperature may loosen or seize at another, depending on how much it grows or shrinks. When designing for a range of operating temperatures, engineers use this formula to predict and compensate for those changes, choosing materials and tolerances that keep the fit acceptable across the expected conditions.

Other forms miss the essential scaling by the original length or mix in the temperature change incorrectly. Omitting L0 would give an incorrect magnitude, and adding deltaT to L0 or misplacing terms doesn’t produce a valid length change.