Question

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. $\frac{200}{3} ^\circ C$
• B. $\frac{100}{3} ^\circ C$
• C. $75 ^\circ C$
• D. $\frac{50}{3} ^\circ C$

Answer 1

Answer: (A)

$\frac{200}{3} ^\circ C$

Answer 2

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