Two rods of material X and two rods of material Y are placed...

Two rods of material $X$ and two rods of material $Y$ are placed with a rod of material $Z$ as shown with the junctions $A$ and $D$ at $100^{\circ} \mathrm{C}$ and $60^{\circ} \mathrm{C}$. Then all rods have equal length (A) Thermal current in $A C$ and $C B$ are equal (B) Thermal current in $A C$ and $A D$ are equal (C) Temperature of $C$ and $D$ are unequal (D) Thermal current in $A C$ and $B D$ is same

Two rods of material $X$ and two rods of material $Y$ are placed with a rod of material $Z$ as shown with the junctions $A$ and $D$ at $100^{\circ} \mathrm{C}$ and $60^{\circ} \mathrm{C}$. Then all rods have equal length
(A) Thermal current in $A C$ and $C B$ are equal
(B) Thermal current in $A C$ and $A D$ are equal
(C) Temperature of $C$ and $D$ are unequal
(D) Thermal current in $A C$ and $B D$ is same

Key Concepts

Thermal Circuit Analysis

Thermal circuit analysis involves modeling complex heat transfer problems using analogies to electrical circuits, where temperature differences act like voltage differences and thermal resistances act like electrical resistors. This approach allows for systematic analysis of heat flows in systems with shared junctions and multiple parallel or series pathways.

Junction Temperature Distribution

In systems where multiple heat conduction pathways meet at a junction, the temperature at that junction is determined by the balance of thermal currents from each branch. Understanding how the junction temperature is established requires analyzing the thermal resistances along each path and ensuring that the net heat flow into the junction is balanced.

Thermal Currents

Thermal currents, or heat currents, describe the rate of heat transfer through a material. They are influenced by the temperature difference between the ends and the thermal resistance of the material, analogous to the current in electrical circuits as described by Ohm's law.

Thermal Resistance

Thermal resistance quantifies how a material opposes heat flow, much like electrical resistance opposes current. It depends on the material’s thermal conductivity and its geometrical dimensions (such as length and cross-sectional area), and is used to simplify the analysis of heat transfer in complex systems.

Thermal Conduction

Thermal conduction is the process by which heat is transferred through a material or between materials in contact. It is governed by Fourier’s law, which states that the rate of heat transfer is proportional to the negative gradient of temperatures and the material's thermal conductivity.

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