A bar of gold (Au) is in thermal contact with a bar of...

A bar of gold $(\mathrm{Au})$ is in thermal contact with a bar of silver (Ag) of the same length and area (Fig. P11.61). One end of the compound bar is maintained at $80.0^{\circ} \mathrm{C}$, and the opposite end is at $30.0^{\circ} \mathrm{C}$. Find the temperature at the junction when the energy flow reaches a steady state.

Key Concepts

Junction Temperature in Composite Materials

In systems composed of two or more materials in thermal contact, the junction temperature is the temperature at the interface between different materials. It is determined by the condition that the heat flux must be continuous across the junction, leading to an equilibrium state where the conductive heat transfers in each material are equal.

Thermal Conduction

Thermal conduction is the process by which heat energy is transferred through a material due to a temperature gradient. It involves the movement of energy from regions of high temperature to regions of low temperature through the vibrations of atoms and free electrons.

Thermal Conductivity

Thermal conductivity is a material property that quantifies how efficiently heat is conducted through a material. It plays a critical role in determining the rate of heat transfer in a medium and differs between materials, influencing the overall temperature distribution in composite systems.

Steady State Heat Transfer

Steady state heat transfer occurs when the temperature distribution in a system no longer changes with time, meaning that the heat flow into any part of the system is equal to the heat flow out. This condition simplifies the analysis as it allows the use of constant heat flux relationships along the system.

Fourier's Law

Fourier's Law of heat conduction states that the heat flux is proportional to the negative of the temperature gradient and the material's thermal conductivity. This law forms the foundation for analyzing steady state conduction problems, as it links the material properties to the observed temperature distribution and heat flow.

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