1. Tardigrade
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  4. 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.]

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Q. A metal rod $AB$ of length $10 x$ has its one end $A$ in ice at $0^{\circ} C$ and the other end $B in$ water at $100^{\circ} C$. If a point $P$ on the rod is maintained at $400^{\circ} C$, 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 $\lambda x$ from the ice end $A$, find the value of $\lambda$. [Neglect any heat loss to the surrounding.]Physics Question Image

JEE AdvancedJEE Advanced 2009

Solution:

$\frac{ dm _{ ice }}{ dt }=\frac{ dm _{\text {vapour }}}{ dt }$
$\frac{400\, kS }{\lambda xL _{\text {ice }}}=\frac{300\, kS }{(100-\lambda) xL _{\text {vapour }}}$
$\lambda=9$