JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Heat & Thermodynamics

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Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures

T_{1} = 300 K

and

T_{2} = 100 K

, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are

K_{1}

and

K_{2}

respectively. If the temperature at the junction of the two cylinders in the steady state is

200 K

, then

K_{1} / K_{2} =

____.

Answer: 4

Solution

In steady state, heat flow through both cylinders is equal. Using

\frac{Δ T}{R _{t h}} =

constant, where

R_{t h} = \frac{L}{K A}

\frac{300 - 200}{L / ( K _{1} A _{1} )} = \frac{200 - 100}{L / ( K _{2} A _{2} )}

. This gives

K_{1} A_{1} = K_{2} A_{2}

. Since

A_{1} / A_{2} = (r_{1} / r_{2})^{2} = (1/2)^{2} = 1/4

, we have

K_{1} / K_{2} = A_{2} / A_{1} = 4.00

JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Numerical answer

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JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Heat & Thermodynamics

Solution

More JEE Advanced questions on Heat & Thermodynamics