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 one 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 `540cal//g` and latent heat of melting of ice is `80cal//g`. If the point P is at a distance of `lambdax` from the ice end A, find the value `lambda`. [Neglect any heat loss to the surrounding.]

Answer

9

Explanation

`i_(1) =(400 -0)/((lambdax//kA)), i_(2) = (400 -100)/((10-lambda)x//kA)`
`(i_(1))/(i_(2)) = (((dm)/(dt))L_(f))/(((dm)/(dt))L_(v)) = (L_(f))/(L_(v))`
`(400 //lambdax)/(300//(10-lambda)x) = (80)/(540) rArr lambda = 9`