JEE Main 2025 · Physics · Calorimetry and Heat Transfer · medium

Four rods of the same cross-sectional area A are joined as follows. Rod 1 has thermal conductivity 2k and length 30 cm. Three other identical rods…

Numerical answer

Four rods of the same cross-sectional area

A

are joined as follows. Rod 1 has thermal conductivity

2k

and length

30\ \mathrm{cm}

. Three other identical rods, each of conductivity

k

and length

30\ \mathrm{cm}

, are connected in parallel between the free end of rod 1 and a common cold end. The free end of rod 1 is held at

100^\circ\mathrm{C}

and the cold end at

0^\circ\mathrm{C}

. In steady state the temperature (in

^\circ\mathrm{C}

) of the junction between rod 1 and the parallel group is ______.

Show answer and solution

Answer: 40

Thermal resistance of a rod is

R_{th} = L/(kA)

. For rod 1:

R_1 = \dfrac{30}{2kA} = \dfrac{15}{kA}

. For each parallel rod:

\dfrac{30}{kA}

, and three in parallel give

R_p = \dfrac{10}{kA}

. In steady state the heat current is common, so the temperature drops divide in the ratio of resistances:

\dfrac{100 - T}{T - 0} = \dfrac{R_1}{R_p} = \dfrac{15}{10}

. Hence

100 - T = 1.5\,T

and

T = 40^\circ\mathrm{C}

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