Two sheets of thickness d and 3d are touching | vedclass

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(A) Let $K_1$ and $K_2$ be the thermal conductivities of the thinner sheet (thickness $d$) and the thicker sheet (thickness $3d$) respectively.In stea

Vedclass · Accepted Answer

$1 : 3$

Vedclass · Answer

(A) Let $K_1$ and $K_2$ be the thermal conductivities of the thinner sheet (thickness $d$) and the thicker sheet (thickness $3d$) respectively.In steady state,the rate of heat flow through both sheets is the same:$\frac{dQ}{dt} = \frac{K_1 A (A - B)}{d} = \frac{K_2 A (B - C)}{3d}$Since $A, B, C$ are in arithmetic progression,we have $B - A = C - B$,which implies $A - B = B - C$.Substituting this into the heat flow equation:$\frac{K_1}{d} = \frac{K_2}{3d}$$\frac{K_1}{K_2} = \frac{1}{3}$Thus,the ratio of the thermal conductivity of the thinner sheet to the thicker sheet is $1 : 3$.

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