GATE 2026 IN – Question 51
The emitted radiant energy from a piece of metal was measured using a pyrometer. The temperature was calculated to be $1000^\circ\mathrm C$, assuming a surface emissivity of 0.8. It was later found that the true surface emissivity was 0.7. The actual temperature of the object is nearest to ________ °C.
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Correct answer: (A) 1043
Explanation
The same measured radiant output implies $0.8T_{ind}^4=0.7T_{actual}^4$, using absolute temperature. The indicated temperature is $1000+273.15=1273.15\ \mathrm K$.
Hence $T_{actual}=1273.15(0.8/0.7)^{1/4}\approx1316.37\ \mathrm K$. Subtracting 273.15 gives about $1043.22^\circ\mathrm C$, nearest **1043 °C (A)**.