A metal rod AB of length
10x has its one end
A in ice at
0∘C and the other end (B) in water at
100∘C. If a point P on the rod is maintained at
400∘C, then it is found that equal amounts of water and ice, evaporate and melt respectively per unit time. The latent heat of vaporization of water is
540cal g−1 and the latent heat of fusion of ice is
80cal g−1. If the point P is at a distance of
λx from the end A, find the value of
λ.
(Neglect any heat loss to the surroundings)