Question

Temperature variation under steady state heat conduction across a composite slab of two materials with thermal conductivities $K_1$ and $K_2$ having same cross sectional area is shown in figure. Choose the correct statement.

• A. $K_1>K_2$
• B. $K_1=K_2$
• C. $K_1=0$
• D. $K_1<K_2$

Answer 1

The correct option is D $K_1<K_2$

We know that, rate of heat conduction $\frac{dQ}{dT}=KA\frac{dT}{dx}$
So, for a constant heat flow, we can say that:
$\frac{dT}{dx}\propto \frac{1}{K}$
where $\frac{dT}{dx}$ is the temperature gradient (slope of the lines in the figure)
[As cross sectional area $A$ is constant]

So, by observing the slopes for both slabs, we can say that
$K_1<K_2$
Thus, option (d) is the correct answer.