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 \[T=\left( \frac{200}{3} \right){{\,}^{o}}C\]