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JEE Advanced2009PhysicsThermal Properties of MatterActual

A metal rod A B 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 calg ⁻¹ and latent heat of melting of ice is 80 calg ⁻¹ . If the point P is at a distance of x from the ice end A , find the value

Correct answer

0

Step-by-step solution

Heat will flow both sides from point P . aligned L₁ d m₁ d t & = ( Temperature difference Thermal resistance )₁ & = 400 ( x) / k A L₁ d m₂ d t & = 400-100 (100- ) x / k A aligned In about two equations, aligned & d m₁ d t = d m₂ d t (given) & L₁=80 calg ⁻¹ and L₂=540 calg ⁻¹ aligned Solving these two equations we get =9 .

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