Question

Two identical rods are made of different materials whose thermal conductivities are k₁ and k₂. They are placed end to end between two heat reservoirs at temperature q₁ and q₂. The temperature of the junction of the rod is –

• A. $\frac{\theta_{1} + \theta_{2}}{2}$
• B. $\frac{k_{1}\theta_{1} + k_{2}\theta_{2}}{2}$
• C. $\frac{k_{1}\theta_{2} + k_{2}\theta_{1}}{k_{1} + k_{2}}$
• D. $\frac{k_{1}\theta_{1} + k_{2}\theta_{2}}{k_{1} + k_{2}}$

Answer 1

Answer: (D)

$\frac{k_{1}\theta_{1} + k_{2}\theta_{2}}{k_{1} + k_{2}}$

Answer 2

In series the rate of heat flow is same

$\frac{\theta_{1} - \theta}{\frac{\mathcal{l}}{k_{1}A}}$ = $\frac{\theta - \theta_{2}}{\frac{\mathcal{l}}{k_{2}A}}$ Ž k₁q₁ – k₁q = k₂q – k₂q₂

q = $\frac{k_{1}\theta_{1} + k_{2}\theta_{2}}{k_{1} + k_{2}}$