Thermocouple calibration behavior: over practical ranges, the thermal emf–temperature relationship of most industrial thermocouples is best described as

Introduction / Context:
Thermocouples generate a voltage (emf) due to the Seebeck effect that depends on temperature. Calibration curves are not perfectly linear; understanding their functional form helps in selecting appropriate linearization or compensation methods in transmitters and controllers.

Given Data / Assumptions:

• Common base-metal and noble-metal thermocouples (e.g., J, K, T, S).
• Moderate industrial temperature ranges (not extreme cryogenic or ultra-high temperatures).
• We look for a best simple descriptor used for approximation.

Concept / Approach:
Standard reference tables fit thermocouple emf as polynomials of temperature. Over limited spans, a second-order (parabolic) polynomial provides a good approximation. While small ranges can appear nearly linear, the general behavior across broader ranges is curved. Exponential or square-root forms are not standard for Seebeck emf curves.

Step-by-Step Solution:
Recall that emf E(T) is commonly represented by polynomial fits.Recognize that quadratic terms dominate the lowest-order nonlinearity.Select “Parabolic (quadratic approximation)” as the best descriptor.

Verification / Alternative check:
Published ITS-90 polynomials show multiple coefficients; truncating to second order over moderate spans often gives acceptable error for quick estimates.

Why Other Options Are Wrong:
Linear: Only approximate over narrow ranges.Exponential / Square-root / Logarithmic: Do not reflect standard thermocouple calibration physics.

Common Pitfalls:
Assuming perfect linearity; ignoring reference-junction compensation effects.

Final Answer:
Parabolic (quadratic approximation)