question_answer

Three rods of the same dimension have thermal conductivities 3K, 2K and K. They are arranged as shown in fig. Given below, with their ends at 100oC, 50oC and 20oC. The temperature of their junction is                        [UPSEAT 2002]

A)            \[{{60}^{o}}\]C

B)            \[{{70}^{o}}\] C

C)            50o C

D)            35o C

Correct Answer: B

Solution :

                   Let the temperature of junction be q then according to following figure. H = H1 + H2 Þ \[\frac{3K\times A\times (100-\theta )}{l}=\frac{2KA(\theta -50)}{l}+\frac{KA(\theta -20)}{l}\] Þ 300 ? 3q = 3q ? 120 Þ q = 70°C