Question bank/JEE Main/Physics

Three metal rods of the same material an identicalin all
respects are joined as shown in the figure. The temperatures at the ends
are maintained asindicated. Assuming no loss of heat from thecurved
surfaces of the rods, the temperature at thejunction X inºCis 10n. Find
n.

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Let T be the temperature at the junction.
Let L and A be the length and area of cross-sectionof each rod
respectively.
[IMAGE] $\therefore$ Heat current from Y to X is 
$H_{1} = \frac{KA\left( 90^{\circ}C - T \right)}{L}$
$H_{2} = \frac{KA\left( 90^{\circ}C - T \right)}{L}$
Heat current from X to W is
$H_{3} = \frac{KA\left( T - 0^{\circ}C \right)}{L}$
 At the junction X 
$H_{1} + H_{2} = H_{3}$
$\therefore 90^{\circ}C - T + 90^{\circ}C - T = T$
or $3T = 180^{\circ}C\ or\ T = 60^{\circ}C$

Source: Grass-G / P-08 Physics paper 23 October.docx