1.

A parallel-sided slab is made of two different materials. The upper half of the slab is made of material X, of thermal conductivity lambda, the lower half is made of material Y, of thermal conductivity 2 lambda. In the steady state, the left hand face of the composite slab is at a higher, uniform temperature than the right-hand face, and the flow of heat through the slab is parallel to its shortest sides. What fraction of the total heat flow through the slab passes through material X ?

Answer»

`(1)/(4)`
`(1)/(3)`
`(1)/(2)`
`(2)/(3)`

Solution :We USE `k_(eq)=(k_(1)A_(1)+k_(2)A_(2))/(A_(1)+A_(2)) =(lambda +2lambda)/(2) =(3 lambda)/(2)`
Total HEAT FLOW through slab,
`rArr``H_(1) =(k_(eq)(2A)(Delta T))/(L)`
`rArr``H_(1)=(3 lambda(2A)Delta T) /(2 L)`…(1)
Heat flow through x,
`H_(2) (k_(x)A(Delta T))/(L)`....(2)
`rArr``(H_(2))/(H_(1)) =(lambda A(Delta T)/(L) xx (2L)/(3 lambda(2A)(Delta T)) =(1)/(3)`


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