One end of a copper rod of uniform cross section and of length 1.5 m is kept in contact with ice and the other end with water at 1000C . At what point along its length should a temperature of 2000C  be maintained. So that in steady state, the mass of ice melting be equal to that of the steam produced in the same interval of time? Assuming that the whole system is insulated from the surrounding. Latent heat of fusion of ice and vaporization of water are 80 cal/g and 540 cal/g respectively.