A 2m iron rod of uniform cross section has its one end in contact with ice at `0^@C` and the other end with water at `100^@C` . Find a point along the length of the rod at which a temperature of `150^@C` is maintained so that mass of ice melted is equal to mass of steam produced in the same time. Consider that the system is thermally isolated from the surroundings. Take, Latent heat of ice = 80 cal/g
Latent heat of vapourisation of water = 540 cal/g

Explanation

Let m = mass of ice melted = mass of steam produced
So, ` m xx L_("ice") = (KA (150 - 0) )/(l) ` …..(i)
and `m xx L_("water")= (KA (150 - 100))/(2 - l) ` ….(ii)
`(L_("ice"))/(L_("water")) = (150)/(l) xx (2-l)/(50) xx (3(2-l))/(l) = 6/l - 3`
` therefore 80/540 + 3 = 6/l`
` rArr 3.148 = 6/l or l =(6)/(3.148) = 1.9 m `