A long iron rod initially at a temperature of 20°C has one end dipped in boiling water (100°C) at time, t = 0. The curved surface of the rod is insulated so that heat conduction is one dimensional in the axial direction. The temperature at a distance 100 mm from the dipped end becomes 40°C at time, t = 200 s. The same temperature is achieved at a distance of 200 mm from the dipped end at time ___________________?
Correct answer: D. t = 800 s
- A. t = 283 s
- B. t = 356 s
- C. t = 400 s
- D. t = 800 s
Explanation
For a semi-infinite rod with a suddenly fixed end temperature, temperature depends on x divided by the square root of time. Doubling the distance requires four times the time to reach the same temperature, giving 4 × 200 = 800 s.
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