A metal rod AB of length 10 x 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 per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of `lambdax` from the ice end A, find the value of `lambda` (Neglect any heat loss to the surroundings)

Answer

9

Explanation

`(k(400-0)A)/(L) = m(80) …. (i)`
`(kA(400-100))/((10x-L)) = m(540) …..(ii)`
Divide (i) by (ii) `1080 x = 120L`
`because L = lambdax therefore = lambda = 9`