Two ends of a conducting rod of varying cross-section are...

Two ends of a conducting rod of varying cross-section are maintained at $200^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$ respectively. In steady state (a) temperature difference across $A B$ and $C D$ are equal (b) temperature difference across $A B$ is greater than that of across $C D$ (c) temperature difference across $A B$ is less than that of across $C D$ (d) temperature difference may be equal or different depending on the thermal conductivity of the rod

Two ends of a conducting rod of varying cross-section are maintained at $200^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$ respectively. In steady state
(a) temperature difference across $A B$ and $C D$ are equal
(b) temperature difference across $A B$ is greater than that of across $C D$
(c) temperature difference across $A B$ is less than that of across $C D$
(d) temperature difference may be equal or different depending on the thermal conductivity of the rod

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Fourier's Law of Thermal Conduction

This principle states that the rate of heat transfer through a material is proportional to the negative gradient of temperature and the area perpendicular to the flow. It is typically expressed as Q = -kA (dT/dx), emphasizing the direct relationship between thermal conductivity, cross-sectional area, and temperature gradient. This law is fundamental in understanding how heat is conducted through materials, including those with varying geometrical properties.

Steady-State Heat Conduction

In steady-state heat conduction, the temperature at any point in the medium remains constant over time, implying that the heat flow is also constant throughout the material. Despite variations in the geometry or material properties, the net heat transferred into any segment equals the heat leaving it, ensuring energy conservation within the medium.

Effect of Cross-Sectional Area on Temperature Gradient

In a conductor with a varying cross-section, the temperature gradient adjusts locally to maintain a constant heat flow. Regions with a smaller area require a steeper temperature gradient to compensate for the reduced pathway for heat, whereas regions with a larger area can sustain the same heat flow with a less steep gradient. This concept is critical for analyzing temperature profiles in non-uniform bars or rods.

Transcript

Please give Ace some feedback