A metal rod AB of length 10x has its one end A in ice at 0^(0)C and the other end B in water at 100^(0)C. If a point P on the rod is maintained at 400^(0)C, then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of melting of ice is 80 cal/g and latent heat of evaporation of water is 540 cal/g. If the point P is at a distance of lambda_(x) from the ice, find the value of lambda. (neglect any heat loss to the surroundings)

A metal rod AB of length 10x has its one end A in ice at 0^(0)C and th

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