A metal rod AB of length has its one end A in ice at

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A metal rod AB of length

10x

has its one end A in ice at

0^\circ\text{C}

, and the other end B in water at

100^\circ\text{C}

. If a point P on the rod is maintained at

400^\circ\text{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 \text{ cal/g}

and latent heat of melting of ice is

80 \text{ 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.] [2009]