Question

figure shows the face and interface of composite slab consisting of two materials a and b relation between thermal conductivities of a and b is​

Answer 1

Answer:

(1) $3K_A = 10K_B$ is the relation between conductivities of a and b.

Explanation:

We know that $\frac{Q}{t}= \frac{KA\delta T}{\delta l}$......(1)

As the heat flow(Q) between the two slabs "a" and "b" is the same.

Then, using the equation (1) we get:

$\frac{K_A A_A(T_{100} -T_{70})}{2l}= \frac{K_B A_B(T_{70} -T_{20})}{l}$.

Now inserting the values given in the question we get,

 $\frac{K_A(100-70)}{2l}= \frac{K_B(70 - 20)}{l}$ (Since the area of cross section is same $A_A = A_B$).

⇒ $\frac{30K_A}{2} = \frac{50K_B}{1}$

⇒ $3K_A = 10K_B$

Therefore, (1) $3K_A = 10K_B$ is the correct option.

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