A metal rod `AB` of length `10x` has it one end 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 melting of ice is `80cal//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 surrounding] .
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Answer

9

Explanation

`(dm_("ice"))/(dt)=(dm_("vapour"))/(dt)`
`Q_(1)=(KA400t)/(lambdaX)=mxx80`
`Q_(2)=(KA(400-100)t)/((10-lambda)X)t=mxx540`

Dividing both, `lambda=9`.