The ends of a metre stick are maintained at 100^∘ C and 0^∘ C. One end of a rod is maintained at

step 1 In this question we have given that the ends of a meter stick are maintained at 100 degrees Cels

The ends of a metre stick are maintained at 100^∘ C and 0^∘...

The ends of a metre stick are maintained at $100^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$. One end of a rod is maintained at $25^{\circ} \mathrm{C}$. Where should its other end be touched on the metre stick so that there is no heat current in the rod in steady state?

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Key Concepts

Steady State Heat Conduction

Steady state heat conduction describes a condition where the temperature distribution within a medium becomes constant over time because the heat entering any section of the material is balanced by the heat leaving it. This results in a stable temperature profile where transient effects have decayed, and it is commonly analyzed with fixed boundary temperatures and no internal heat generation.

Linear Temperature Gradient

In systems where the thermal properties are homogeneous and the boundaries are maintained at constant temperatures, the temperature varies linearly along the medium. This linear variation comes from the balance of conduction across the material as dictated by Fourier’s law, and it allows for the use of simple interpolation to determine the temperature at any intermediate point.

Thermal Equilibrium

Thermal equilibrium occurs when two objects or parts of a system that are in thermal contact reach the same temperature, resulting in no net heat transfer between them. In the context of conduction problems, ensuring that the contact point between a rod and a medium shares the same temperature means that there is no driving force for heat to flow, satisfying the condition of thermal equilibrium.

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