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.]

Options

A. 9
B. 2
C. 6
D. 1

Answer

A

Explanation

(1) `R_(1) = (10 x - lambda x)/(KA), R_(2) = (lambda x)/(KA)`
`i_(1) = (400 - 100)/(R_(1)) = mL_(steam)`
`i_(2) = (400 - 0)/(R_(2)) = m L_(ice)`
(i), (ii) `implies (3)/(4) (R_(2))/(R_(1)) = (L_(steam))/(L_(ice))`
(i) `(3)/(4) . ((lambda)/(10 - lambda)) = (540)/(80) = (27)/(4)`
`(lambda)/(10 - lambda) = 9 implies - 9 lambda`
`lambda = 9`