JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Heat & Thermodynamics

Two metallic blocks

M_{1}

and

M_{2}

of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of

M_{2}

is K then the thermal conductivity of

M_{1}

will be : [Assume steady state heat conduction]

Answer: (B)

Solution

In steady state, the heat flow rate through both blocks is the same. The thermal resistance is

R = \frac{ℓ}{k A}

, and temperature drop is proportional to thermal resistance.

From the figure:

Δ T_{1} = 20°

Δ T_{2} = 80°

ℓ_{1} = 16

cm,

ℓ_{2} = 8

cm.

\frac{Δ T _{1}}{Δ T _{2}} = \frac{R _{1}}{R _{2}} = \frac{ℓ _{1} / k _{1}}{ℓ _{2} / k _{2}}

\frac{20}{80} = \frac{16}{k _{1}} \times \frac{k}{8}

\frac{1}{4} = \frac{2 k}{k _{1}} \Rightarrow k_{1} = 8 k

The answer is (B) 8K.

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Single correct option