The ends of a uniform metre stick of iron are maintained at 80^∘ C and 30^∘ C. One end of anothe

step 1 In the given question, we are required to find out such a point on this part where the other end

The ends of a uniform metre stick of iron are maintained at...

The ends of a uniform metre stick of iron are maintained at $80^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$. One end of another rod is maintained at $50^{\circ} \mathrm{C}$, where its other end should be touched on the metre stick so that there is no heat current in the rod in steady state? (A) $40 \mathrm{~cm}$ from hot end (B) $40 \mathrm{~cm}$ from cold end (C) $50 \mathrm{~cm}$ from cold end (D) $70 \mathrm{~cm}$ from cold end

The ends of a uniform metre stick of iron are maintained at $80^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$. One end of another rod is maintained at $50^{\circ} \mathrm{C}$, where its other end should be touched on the metre stick so that there is no heat current in the rod in steady state?
(A) $40 \mathrm{~cm}$ from hot end
(B) $40 \mathrm{~cm}$ from cold end
(C) $50 \mathrm{~cm}$ from cold end
(D) $70 \mathrm{~cm}$ from cold end

Key Concepts

Thermal Equilibrium

Thermal equilibrium is the state where two systems in contact no longer exchange heat because they are at the same temperature. In this context, when connecting a rod that is maintained at a particular temperature to a point on another object, no net heat flow occurs if the contact point is at the same temperature, achieving local thermal equilibrium.

Steady State Heat Conduction

This concept refers to the condition in which the temperature distribution in a material does not change with time. In steady state, the heat entering and leaving any part of the system is balanced, leading to a constant temperature profile. This allows for the use of linear temperature gradients in one-dimensional conduction problems.

Fourier’s Law of Heat Conduction

Fourier’s Law states that the rate of heat transfer through a material is proportional to the negative gradient of temperature and the area through which the heat flows. This law is fundamental for determining how heat flows in a system with a linear temperature distribution, particularly in determining points of thermal equilibrium.

Linear Temperature Distribution

In a uniform rod with fixed temperatures at the ends, the temperature varies linearly along its length under steady state conditions. This linearity enables one to interpolate or determine the temperature at any given point along the rod by considering its fraction of the total length between the hot and cold ends.

Transcript

Please give Ace some feedback