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 λ x from the ice end A, find the value of λ. [Neglect any heat loss to the surrounding.]

Question

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 λ x from the ice end A, find the value of λ. [Neglect any heat loss to the surrounding.] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

( dm ice / dt )=( dm text vapour / dt ) (400 kS /λ xL text ice )=(300 kS /(100-λ) xL text vapour ) λ=9

dtdmice​​=dtdmvapour ​​ λxLice ​400kS​=(100−λ)xLvapour ​300kS​ λ=9

$\frac{d m _{i ce}}{d t} = \frac{d m _{vapour}}{d t}$
$\frac{400 k S}{λ x L _{ice}} = \frac{300 k S}{( 100 - λ ) x L _{vapour}}$
$λ = 9$