Two metallic blocks M1 and M2 of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M2 is K then the thermal conductivity of M1 will be : [Assume steady state heat conduction]

Heat and Thermodynamics PYQ — JEE Main 2022 · 24 Jun · Shift 1 · Q61 with Solution

View written solutionFree

Correct answer: B

Steady state heat conduction principle
In steady state, the rate of heat flow through both metallic blocks connected in series is the same.

For a slab,

\frac{Q}{t} = \frac{kA\Delta T}{L}

where:

Since both blocks have the same cross-sectional area and are in series, we can write:

\frac{k_1 \Delta T_1}{L_1} = \frac{k_2 \Delta T_2}{L_2}

Using the figure information
From the given figure, the ratio of lengths and temperature drops is:

\frac{k_1}{k_2} = \frac{L_1}{L_2}\cdot \frac{\Delta T_2}{\Delta T_1}

The figure implies:

\frac{L_1}{L_2} = 2

and

\frac{\Delta T_2}{\Delta T_1} = 4

Therefore,

\frac{k_1}{k_2} = 2 \times 4 = 8

Since $k_2 = K$ ,

k_1 = 8K

Hence, the correct option is:

\boxed{8K}