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.]

Explanation

`((DeltaQ)/(Deltat))_(l)=(300)/((10x-lamdax)/(KA))=mL_(v)`.....(1)
and `((DeltaQ)/(Deltat))_(w)=(400)/((lamdax)/(KA))=mL_(f)` ....(2)
dividing `(300)/(10x-lambdax)xx(lambdax)/(400)=(L_(v))/(L_(f))`
`implies(3)/(4)(lambda)/((10-lambda))=(540)/(80)lambda=9(10-lambda)10lambda=90implieslambda=9`