Consider a pair of insulating blocks with thermal resistances \( R_1 \) and \( R_2 \) as shown in the figure. The temperature \( \theta \) at the boundary between the two blocks is:
Show Hint
In heat transfer through materials with different thermal resistances, the temperature at the boundary is proportional to the resistances.
Step 1: Understanding thermal resistance.
In a steady-state heat transfer situation, the temperature at the interface is determined by the thermal resistances of the materials. The relation between the temperatures and resistances is:
\[
\frac{\theta_2}{\theta_1} = \frac{R_2}{R_1 + R_2}
\]
Step 2: Conclusion.
Thus, the temperature \( \theta_2 \) at the boundary between the blocks is given by:
\[
\theta_2 = \frac{R_2}{R_1 + R_2} \theta_1
\]
Final Answer:
\[
\boxed{\theta_2 = \frac{R_2}{R_1 + R_2} \theta_1}
\]
