The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thicknesses x and 4x, respectively are `T_(2)` and `T_(1)(T_(2)gtT_(1))`. The rate of heat of heat transfer through the slab, in ? steady state is `[(A(T_(2)-T_(1))/(x)]f`, with f equal to :-

Options

A. 1
B. `1//2`
C. `2//3`
D. `1//3`

Answer

D

Explanation

For slab in series , we have
`R _(eq) = R_(1) + R_(2) = (x)/(KA) +(4x)/(2KA) =(3x)/(kA)`
Now , in a steady state rate of heat transfer throught the slab is given by .
`(dQ)/(dt) = (T_(2) -T_(1))/(R_(eq)) = ((T_(1)-T_(1)))/(3x) KA" "...(i)`
Given `(dQ)/(dt) = ((A(T_(2) - T_(1)))/(x))f " "....(ii)`
Comparing (i) and (ii) we get `f = 1//3`