question_answer

Three rods made of same material and having same cross-section are joined as shown in the figure. Each rod is of same length. The temperature at the junction of the three rods is

A)  \[{{45}^{o}}C\]            

B)         \[{{90}^{o}}C\]

C)         \[{{30}^{o}}C\]            

D)         \[{{20}^{o}}C\]

E)  \[{{60}^{o}}C\]

Correct Answer: E

Solution :

Let the temperature of junction be\[\theta ,\]then \[H={{H}_{1}}+{{H}_{2}}\] \[\Rightarrow \]               \[\frac{KA(\theta -0)}{L}=\frac{KA(90-\theta )}{L}+\frac{KA(90-\theta )}{L}\] or        \[\theta =90-\theta +90-\theta \] or       \[\theta =180-26\] or       \[3\theta =180\] or       \[\theta =60{}^\circ C\]