One end of conducting rod is maintained at temperature `50^(@)C` and at the other end ice is melting at `0^(@)C`. The rate of melting of ice is doubled if:

Options

A. the temperature is made `200^(@)C` and the area of cross-section of the rod is doubled
B. the temperature is made `100^(@)C` and the length of the rod is made four time
C. area of cross-section of the rod is halved and length is doubled.
D. the temperature is made `100^(@)C` and area of cross-section of rod and length both are doubled.

Answer

D

Explanation

Rate of melting ice `prop` rate of heat transfer `(dQ//dt)`
Further `(dQ)/(dt) = ("temperature difference")/((l//KA))`
or `(dQ)/(dt) = ("temp. Diff.")/(l) xx A`
If temp. Diff. `A` and `l` are all doubled, then `dQ//dt`, and hence rate of melting of ice, are doubled.