Bimetallic thermometer behavior: the deflection of the free end of a bimetal strip versus temperature change is, over its normal operating range, approximately which functional form?

Introduction / Context:
A bimetallic thermometer uses two metals with different coefficients of thermal expansion bonded together. Temperature change creates differential expansion, bending the strip and producing a pointer deflection. Understanding the approximate deflection-temperature relationship helps with calibration and scale layout.

Given Data / Assumptions:

• Small to moderate temperature spans within design limits.
• Linear thermal expansion coefficients assumed constant over the range.
• Uniform strip properties and constant curvature approximation.

Concept / Approach:
When the expansion coefficients are treated as constant and strains are within elastic limits, the curvature of a bimetal strip is proportional to the temperature difference, leading to a nearly linear relation between tip deflection and temperature. While exact mechanics involve composite-beam theory, for practical thermometer ranges the scale is laid out linearly, and deviations are minor.

Step-by-Step Solution:

Verification / Alternative check:
Calibration charts for commercial bimetallic thermometers show straight-line scales over their rated ranges; strong nonlinearity appears only at extremes or with nonuniform materials.

Why Other Options Are Wrong:

Common Pitfalls:
Assuming perfect linearity at all temperatures; materials change properties with temperature, causing slight deviations near limits.

Final Answer:
Linear