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