High-temperature measurement: a radiation pyrometer operates fundamentally according to which physical law relating radiated energy to temperature?

Introduction / Context:
Radiation pyrometers measure temperature of hot objects without contact by sensing thermal radiation. Understanding the governing radiation laws is vital in furnace control, metallurgy, and materials processing.

Given Data / Assumptions:

• Total (integrating) radiation pyrometers measure emitted energy over a broad band.
• Emissivity is accounted for or approximated.
• Objects are sufficiently hot for significant thermal emission.

Concept / Approach:
The Stefan–Boltzmann law states that total radiated power per unit area is proportional to T^4 (for a blackbody): E = σ T^4; for real surfaces, E = ε σ T^4. Total radiation pyrometers exploit this relationship. Optical (narrow-band) pyrometers often rely on Planck’s law and use approximations such as Wien’s law, but “radiation pyrometer” in general industrial usage most commonly refers to total radiation, hence Stefan–Boltzmann law applies fundamentally.

Step-by-Step Solution:
Measure radiant flux from target.Account for instrument view factor and emissivity (ε).Relate measured power to temperature via E ∝ T^4.

Verification / Alternative check:
Two-color/ratio pyrometers minimize emissivity uncertainty but still derive from Planckian emission; in contrast, total radiation units explicitly integrate and back-calculate temperature using T^4 scaling—consistent with Stefan–Boltzmann.

Why Other Options Are Wrong:

• Wien’s law: relates wavelength of peak emission to temperature; used in optical pyrometry but not the basis of total energy measurement.
• Kirchhoff’s law: links emissivity and absorptivity; supportive, not the direct operative law.
• Seebeck effect: thermoelectric principle for contact thermocouples, not radiation pyrometers.

Common Pitfalls:
Ignoring emissivity leads to temperature errors; reflective or oxidized surfaces can change ε significantly.

Final Answer:
Stefan–Boltzmann law