JEE Advanced · 2009 · 12 Apr 2009 · Paper 2 · Heat & Thermodynamics

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

10 0^{\circ} C

. If a point P on the rod is maintained at

40 0^{\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

λ x

from the ice end A, find the value of

λ

.
[Neglect any heat loss to the surrounding.]

Answer: 9

Solution

Let the rate of heat flow be equal on both sides. From A to P:

\frac{d m _{i ce}}{d t} \cdot L_{i ce} = \frac{k S \cdot 400}{λ x}

. From P to B:

\frac{d m _{v a p o u r}}{d t} \cdot L_{v a p o u r} = \frac{k S \cdot 300}{( 10 - λ ) x}

. Since the rates are equal:

\frac{400}{λ \cdot 80} = \frac{300}{( 10 - λ ) \cdot 540}

. Solving:

400 \cdot 540 \cdot (10 - λ) = 300 \cdot 80 \cdot λ

, which gives

λ = 9

JEE Advanced · 2009 · 12 Apr 2009 · Paper 2 · Integer answer

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JEE Advanced · 2009 · 12 Apr 2009 · Paper 2 · Heat & Thermodynamics

Solution

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