One end of a copper rod of uniform cross-section and of length $1.5\text{ m}$ is kept in contact with ice at $0^\circ\text{C}$ and the other end with water at $100^\circ\text{C}$. If the whole system is insulated from its surroundings, then at what distance from the end of the rod which is in contact with the steam should the temperature be maintained at $200^\circ\text{C}$, so that in steady-state the rate of melting of ice equals the rate of production of steam? $[L_{\text{fusion}} = 80\text{ cal g}^{-1},\; L_{\text{vaporization}} = 540\text{ cal g}^{-1}]$