Two plates each of area `A` thickness `L_(1)` and `L_(2)` thermal conductivities `K_(1)` and `K_(2)` respectively are joined to from a single plate of thickness `(L_(1)+L_(2))` If the temperatures of the free surfaces are `theta_(1)` and `theta_(2)` Calculate
(a) Rate of flow of heat
(b) Temperature of interface
.

Explanation

If the thermal resistance of the two plates are `R_(1)` and `R_(2)` respectively then as plates are in series
`R_(s)=R_(1)+R_(2)=(L_(1))/(AK_(1))+(L_(2))/(AK_(2))`
`H=(dQ)/(dt) = (Deltatheta)/(R_(s))=((theta_(1)-theta_(2)))/((R_(1)+R_(2)))=(A(theta_(1)=theta_(2)))/([(L_(1))/(K_(1))+(L_(2))/(K_(2))]`
(b) If `theta` is common temperature of interface then
`(theta_(1)-theta_(2))/(R_(1)+R_(2))=(theta_(1)-theta)/(R-1)[:'H_(1)=H_(2)]:.theta=(theta_(1)R_(2)+theta_(2)R_(1))/((R_(1)+R_(2)))`
`theta=[[theta_(1)(L_(2))/(K_(2))+theta_(2)(L_(1))/(K_(1))]]/([L_(1)/(K_(1))+(L_(2))/(K_(2))])[:'R=(L)/(KA)]` .