Optical pyrometry – disappearing filament type The working principle of the disappearing-filament optical pyrometer is based primarily on which radiation law?

Introduction / Context:
Optical pyrometers measure high temperatures by comparing the brightness of a hot object to that of a calibrated filament. The disappearing-filament type is widely referenced in instrumentation courses and relies on the temperature dependence of monochromatic radiance.

Given Data / Assumptions:

• Instrument: disappearing-filament optical pyrometer.
• Measurement: brightness matching at a selected wavelength.
• Hot body approximated as a gray body; calibration links brightness to temperature.

Concept / Approach:
Wien’s law (in its radiation form) captures how spectral radiance varies strongly with temperature at short wavelengths, enabling brightness temperature determination by matching the filament brightness to the target at a fixed wavelength. When the filament “disappears” against the background (same apparent brightness), the instrument reads the corresponding temperature. Seebeck and Peltier effects are thermoelectric phenomena, not radiation laws. Kirchhoff’s law relates emissivity and absorptivity but does not provide the operational brightness–temperature relation exploited for matching.

Step-by-Step Solution:

Verification / Alternative check:
Instrument manuals describe “brightness temperature” and its reliance on the exponential temperature dependence from Wien’s radiation law at short wavelengths.

Why Other Options Are Wrong:

• Seebeck / Peltier: Concern electromotive force or heat at junctions, not optical radiation.
• Kirchhoff's law: Important for emissivity–absorptivity equality at thermal equilibrium, but not the basis of the brightness comparison method.

Common Pitfalls:
Confusing Wien’s displacement law (peak wavelength shift) with the brightness law; the measurement uses the strong temperature dependence of spectral radiance at fixed wavelength.

Final Answer:
Wien's law