Step 1: Understanding the Question:
The question asks to identify the fundamental physical law that governs the operation of a radiation pyrometer.
Step 2: Detailed Explanation:
• A radiation pyrometer is a non-contact temperature measuring device that estimates the temperature of a hot body by measuring the thermal radiation emitted from its surface.
• According to blackbody radiation physics, every object at a temperature above absolute zero emits electromagnetic radiation.
• The Stefan-Boltzmann Law states that the total radiant energy ($E$) emitted per unit area of a blackbody per unit time is directly proportional to the fourth power of its absolute temperature ($T$):
\[ E = \sigma T^4 \]
where $\sigma$ is the Stefan-Boltzmann constant.
• For a non-blackbody with emissivity $\epsilon$, the relationship is:
\[ E = \epsilon \sigma T^4 \]
• Radiation pyrometers focus the emitted thermal radiation onto a detector (such as a thermopile). The electrical output of the detector is calibrated to represent the absolute temperature of the target source based on this fourth-power relationship.
• Thus, the operating principle is directly based on Stefan-Boltzmann's Law.
Step 3: Final Answer:
The principle of a radiation pyrometer is based on the Stefan-Boltzmann Law.