To determine the temperature at the junction
x of three identical metal rods, follow this analysis:
Assuming No Heat Loss: The rods are made of the same material and are identical, ensuring consistent heat flow throughout.
Thermal Resistance: Let the thermal resistance of each rod be
R. The temperature at the junction is
Tx.
Heat Flow Equilibrium: Since the system reaches a steady state, the heat flowing into the junction from each side should equal the heat flowing out:
H=H1+H2 Where:
H is the heat flowing into the junction from both ends.
H1 and
H2 are the heat flows from the sides of the junction.
Application: Set up the heat balance equation:
‌=‌+‌Simplifying: Substitute and solve:
Tx=‌=60∘C Therefore, the temperature at the junction
x is
60∘C. This calculation assumes perfect thermal conduction and no heat loss outside the system.