A Rod, with Sides Insulated to Prevent Heat Loss, Has $100 ^ { \circ } \mathrm { C }$

Short Answer

A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water at $100 ^ { \circ } \mathrm { C }$ and the other end in a water-ice mixture at $0 ^ { \circ } \mathrm { C }$ The rod has uniform cross-sectional area $7.05 \mathrm {~cm} ^ { 2 }$ and length 87 cm. The heat conducted by the rod melts the ice at a rate of 1.0 g every 11 seconds. What is the thermal conductivity of the rod? Recall that the heat of fusion of water is $3.34 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$