Question

Explain why an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open but gives a correct value for the temperature when the same piece is in the furnace.

Answer 1

Hint: An optical pyrometer relates the brightness of a glowing body with its temperature. It works on the principle of matching the brightness of an object to the brightness of the filament which is placed inside the pyrometer.

Complete step by step answer:
An optical pyrometer calibrated for an ideal black body radiation gives too low a value for temperature of a red-hot iron piece that is kept in the open space.

The black body radiation equation is as,
\[\text{E}=\sigma \left( {{\text{T}}^{4}}-\text{T}_{0}^{4} \right)\]
Where, E is energy radiation, T is temperature of optical pyrometer, \[\text{T}_{0}^{{}}\]is temperature of open space and \[\text{ }\!\!\sigma\!\!\text{ }\] is Stefan’s constant.

Now, from the above-mentioned formula, it is clearly shown that an increase in the temperature of open space reduces the radiation energy. When the same piece of iron is placed in a furnace, the radiation energy, that is \[\text{E}=\text{ }\!\!\sigma\!\!\text{ }{{\text{T}}^{4}}\].

Note:
In the open because of other sources of light the sensor in the optical pyrometer does not detect the true brightness of a red-hot piece of iron and thus does not predict its temperature correctly whereas in the furnace the piece of iron is the only source of light and the sensor detects its brightness correctly thus giving the correct value of the temperature.