A metal rod $AB$ of length $10x$ has its one end $A$ in ice at $0℃$ and the other end $B$ in water at $100℃$. If a point $P$ on the rod is maintained at $400℃$, 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 $540\ cal/g$ 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]

Question

Dr. Abubacker · Accepted Answer

(a) [image:11_image58.emf]
Hear received by end $A$, for melting of ice
$Q_{A} = \frac{K\ A(400 - 0)t}{\lambda \bullet x} = m\ L_{ice}$ …(i)
Heat received by end $B$, for vaporization of water
$Q_{B} = \frac{K\ A(400 - 100)t}{(10 - \lambda)x} = m\ L_{vap}$ …(i)
Dividing both equation, $\frac{\frac{400}{\lambda \bullet x}}{\frac{300}{(10 - \lambda)x}} = \frac{L_{ice}}{\ L_{vap}}$
$\Rightarrow \frac{4}{3}\frac{(10 - \lambda)}{\lambda} = \frac{80}{540} \Rightarrow \lambda = 9$

Explanation

Reviewed by Dr. Abubacker

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