A rod CD of thermal resistance $10.0 \mathrm{KW}^{-1}$ is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at $200^{\circ} \mathrm{C}$, $100^{\circ} \mathrm{C}$ and $125^{\circ} \mathrm{C}$ respectively. The heat current in CD is P watt. The value of $P$ is ______.

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Heat & Thermodynamics

A rod CD of thermal resistance

10.0 KW^{- 1}

is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at

20 0^{\circ} C

10 0^{\circ} C

and

12 5^{\circ} C

respectively. The heat current in CD is P watt. The value of

P

is ______.

Answer: 2

Since

A B

is identical to

C D

, its full thermal resistance is

10 K W^{- 1}

and each half,

A C

and

C B

, has resistance

5 K W^{- 1}

. Let the junction

C

be at temperature

T_{C}

. Conservation of heat current at

C

gives

\frac{200 - T _{C}}{5} = \frac{T _{C} - 100}{5} + \frac{T _{C} - 125}{10} .

Multiplying through by

10

yields

2 (200 - T_{C}) = 2 (T_{C} - 100) + (T_{C} - 125)

, so

725 = 5 T_{C}

and

T_{C} = 14 5^{\circ} C

. The heat current in

C D

P = \frac{T _{C} - 125}{10} = \frac{145 - 125}{10} = 2 W .

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Integer answer