question_answer

Three rods of same dimensions have thermal conductivities 3 K, 2 K and K. They are arranged as shown below: What will be the temperature T of the junction?

A)  \[\frac{200}{3}\] °C                                        

B)  \[\frac{100}{3}\] °C

C)   75°C                                    

D)  \[\frac{50}{3}\] °C

Correct Answer: A

Solution :

  Rate of flow of heat \[H={{H}_{1}}+{{H}_{2}}\]                 \[\frac{3K.(T-100)A}{l}=\frac{2K(50-T)A}{l}+\frac{K(0-T)A}{l}\]                 \[\therefore \]  \[3T-300=100-2T-T\] or            \[6T=400\] or            \[T=\left( \frac{200}{3} \right){{\,}^{o}}C\]