Question 392: Thermodynamics & KTG

Question

Two materials having coefficients of thermal
conductivity '3K' and 'K' and thickness 'd' and
'3d', respectively, are joined to form a slab as
shown in the figure. The temperatures of the
outer surfaces are '$	heta $
2
' and '$	heta $
1
' respectively,
($	heta $
2
> $	heta $
1
). The temperature at the interface is :-
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lkxi0niu/e5f746fa-d0cb-4210-8720-c211cc424c41/45764450-3346-11ee-bd20-af65b033e504/file-6y3zli1lkxi0niv.png?format=png)

Accepted Answer

Let interface temperature in steady state conduction is $	heta$, then assuming no heat loss through sides;
$
\left(\begin{array}{l}
	ext { Rate of heat } \
	ext { flow through } \
	ext { first slab }
\end{array}ight)=\left(\begin{array}{l}
	ext { Rate of heat } \
	ext { flow through } \
	ext { second slab }
\end{array}ight)
$
$
\begin{aligned}
& \Rightarrow \frac{(3 K) A\left(	heta_2-	hetaight)}{d}=\frac{K A\left(	heta-	heta_1ight)}{3 d} \\
& \Rightarrow \quad 9\left(	heta_2-	hetaight)=	heta-	heta_1 \\
& \Rightarrow \quad 9 	heta_2+	heta_1=10 	heta \\
& \Rightarrow \quad 	heta=\frac{9}{10} 	heta_2+\frac{1}{10} 	heta_1
\end{aligned}
$

Answer

${{{	heta _1}} \over {10}} + {{9{	heta _2}} \over {10}}$

Answer

${{{	heta _2} + {	heta _1}} \over 2}$

Answer

${{{	heta _1}} \over {6}} + {{5{	heta _2}} \over {6}}$

Answer

${{{	heta _1}} \over {3}} + {{2{	heta _2}} \over {3}}$

Thermodynamics & KTG

Choose the correct answer: