Figure shows a copper rod joined to a steel rod. The rods...

Figure shows a copper rod joined to a steel rod. The rods have equal length and equal cross-sectional area, The free end of the copper rod is kept at $0^{\circ} \mathrm{C}$ and that of the steel rod is kept at $100^{\circ} \mathrm{C}$. Find the temperature at the junction of the rods. Conductivity of copper $=390 \mathrm{~W} / \mathrm{m}-{ }^{\circ} \mathrm{C}$ and that of steel $=46 \mathrm{~W} / \mathrm{m}-{ }^{\circ} \mathrm{C}$

Key Concepts

Thermal Resistance

Thermal resistance is a concept that represents the opposition to heat flow through a material or across an interface. It is analogous to electrical resistance in an electric circuit and helps simplify the analysis of heat conduction in composite systems by allowing the calculation of temperature drops across different materials.

Steady-State Heat Transfer

In a steady-state condition, the temperature distribution within a system remains constant over time, and the heat flow into any part of the system is balanced by the heat flowing out. This concept is critical for analyzing systems where heat transfer parameters do not change with time.

Thermal Conductivity

Thermal conductivity is a material-specific property that measures its ability to conduct heat. Materials with high thermal conductivity transfer heat quickly, whereas materials with low thermal conductivity are better insulators. This property is essential when analyzing heat transfer in composite systems.

Fourier's Law of Heat Conduction

Fourier's Law quantitatively describes the conduction of heat through a material. It establishes that the heat transfer rate is proportional to the negative gradient of temperature and the area through which heat flows, with the proportionality constant being the material's thermal conductivity.

Thermal Conduction

Thermal conduction is the process by which heat energy is transferred within a material or between materials in direct contact. It involves the movement of energy from regions of higher temperature to regions of lower temperature due to the collisions and vibrations of particles in the material.

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