Question

Three metal rods of the same material and identical in all respects are joined as shown in the figure. The temperatures at the ends are maintained as indicated.

Assuming no loss of heat from the curved surfaces of the rods, the temperature at the junction X would be

• A. 45°C
• B. 60°C
• C. 30°C
• D. 20°C

Answer 1

Answer: (B)

60°C

Answer 2

Let T be the temperature at the junction. Let L and A be the length and area of cross sections of each and respectively.

$\therefore$Heat current from Y to X is

$H_{1} = \frac{K_{A}(90{^\circ}C - T)}{L}$

Heat current from Z to X is

$H_{2} = \frac{KA(90{^\circ}C - T)}{L}$

Heat current form X to W is

$H_{3} = \frac{KA(T - 0{^\circ}C)}{L}$

At the junctions x, $H_{1} + H_{2} = H_{3}$

$\therefore 90{^\circ}C = T + 90{^\circ}C - T = T$Or 3T = $180{^\circ}C$

Or $T = 60{^\circ}C$