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One end of a conducting rod is held at 50 deg C while the other end keeps ice melting at 0 deg C. The rate of melting of ice is doubled if:

1. the hot-end temperature is made 200 deg C and the cross-sectional area is doubled
2. the hot-end temperature is made 100 deg C and the length is made four times
3. the cross-sectional area is halved and the length is doubled
4. the hot-end temperature is made 100 deg C and both the cross-sectional area and length are doubled

Correct answer: the hot-end temperature is made 100 deg C and both the cross-sectional area and length are doubled

Solution

Heat current = kA*deltaT/L; for option D the factor is (100/50)*(2)*(1/2) = 2, exactly doubling the rate.

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