GATE 2026 CH – Question 51
A thermometer initially at a steady temperature of 30 °C is inserted in a water bath maintained at 90 °C. The initial rate of temperature rise of the thermometer is 2 °C s$^{-1}$. Assuming first order behavior, the thermometer reading (in °C) after one minute is ______ (rounded off to one decimal place).
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Correct answer: 81.49 to 82.31
Explanation
For a first order response $T = 90 - 60e^{-t/\tau}$. The initial rate is $\frac{60}{\tau} = 2$ °C/s, so $\tau = 30$ s. After 60 s, $T = 90 - 60e^{-2} = 90 - 8.12 = 81.9$ °C.