question_answer

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

A)  \[\frac{200}{3}{}^\circ C\]                  

B)  \[\frac{100}{3}{}^\circ C\]

C)  \[75\,{}^\circ C\]                     

D)  \[\frac{50}{3}\,{}^\circ C\]

Correct Answer: A

Solution :

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