JEE Main 2019 · Physics · Calorimetry and Heat Transfer · medium

A composite rod is made of a copper section and a steel section, each 20 cm long and of cross-sectional area 2 cm^2, joined end to end and lagged so…

Single correct option

A composite rod is made of a copper section and a steel section, each

20\ \mathrm{cm}

long and of cross-sectional area

2\ \mathrm{cm^2}

, joined end to end and lagged so that heat flows only along its length. The free end of the copper is held at

100^\circ\mathrm{C}

and the free end of the steel at

0^\circ\mathrm{C}

. The thermal conductivities of copper and steel are

360

and

40\ \mathrm{W\,m^{-1}K^{-1}}

. In the steady state the rate of heat flow through the rod is

Show answer and solution

Answer: (B) $3.6\ \mathrm{W}$

In the steady state the same heat current flows through both sections, which behave as thermal resistances in series,

R_{th}=\dfrac{L}{kA}

. Copper:

\dfrac{0.2}{360\times2\times10^{-4}}=2.78\ \mathrm{K\,W^{-1}}

. Steel:

\dfrac{0.2}{40\times2\times10^{-4}}=25\ \mathrm{K\,W^{-1}}

. The total is

27.78\ \mathrm{K\,W^{-1}}

, so

H=\dfrac{100}{27.78}=3.6\ \mathrm{W}

. The interface temperature is

90^\circ\mathrm{C}

(the drop is nine times larger across steel). Using the steel half alone with the full

100^\circ\mathrm{C}

difference would give

4.0\ \mathrm{W}

Original question written in the JEE Main 2019 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake