Question

The temperature of the interface of a compound wall as shown in the figure, in terms of their thermal resistances R₁ and R₂ is

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

Answer 1

Answer: (B)

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

Answer 2

Temperature of interface $\theta = \frac{K_{1}\theta_{1} + K_{2}\theta_{2}}{K_{1} + K_{2}}$

Substituting $K_{1} = \frac{l}{R_{1}A}$ and $K_{2} = \frac{l}{R_{2}A}$ we get

$\theta = \frac{R_{1}\theta_{2} + R_{2}\theta_{1}}{R_{1} + R_{2}}$.