GATE 2022 MN – Question 43
A thermometer initially reads 2°C and is moved into a room at 40°C. Its heating rate is proportional to the room–thermometer temperature difference. After 2 min it reads 15°C. Find elapsed time from entry until it reads 39.5°C, in minutes to two decimals.
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Correct answer: 20.40 to 20.80
Explanation
Newton’s law gives 40−T=38 exp(−kt). After two minutes, the temperature difference is 25°C, so exp(−2k)=25/38. At 39.5°C the difference is 0.5°C. Taking the ratio of logarithms gives t=2 ln(38/0.5)/ln(38/25)=20.6861 minutes, or 20.69 minutes. This is total elapsed time from entry into the room.