One end of a metal rod of length 1.0 m and area of cross-section 100 cm^2 is maintained at 100

step 1 In this question we will learn about some basic concept of the heat transfer. The question is we

One end of a metal rod of length 1.0 m and area of...

One end of a metal rod of length $1.0 \mathrm{~m}$ and area of cross-section $100 \mathrm{~cm}^{2}$ is maintained at $100^{\circ} \mathrm{C}$. If the other end of the rod is maintained at $0^{\circ} \mathrm{C}$, the quantity of heat transmitted through the rod per minute is; (Coefficient of thermal conductivity of material of the rod $=100 \mathrm{~W} / \mathrm{kg} / \mathrm{K}$ ) (a) $3 \times 10^{3} \mathrm{~J}$ (b) $6 \times 10^{3} \mathrm{~J}$ (c) $9 \times 10^{3} \mathrm{~J}$ (d) $12 \times 10^{3} \mathrm{~J}$

One end of a metal rod of length $1.0 \mathrm{~m}$ and area of cross-section $100 \mathrm{~cm}^{2}$ is maintained at $100^{\circ} \mathrm{C}$. If the other end of the rod is maintained at $0^{\circ} \mathrm{C}$, the quantity of heat transmitted through the rod per minute is; (Coefficient of thermal conductivity of material of the rod $=100 \mathrm{~W} / \mathrm{kg} / \mathrm{K}$ )
(a) $3 \times 10^{3} \mathrm{~J}$
(b) $6 \times 10^{3} \mathrm{~J}$
(c) $9 \times 10^{3} \mathrm{~J}$
(d) $12 \times 10^{3} \mathrm{~J}$

Key Concepts

Heat Conduction

Heat conduction is the process by which thermal energy is transferred within a body or between bodies in direct contact, due to a temperature difference. This conduction mechanism occurs primarily in solids where particles interact through lattice vibrations, transferring energy without any bulk movement of the material.

Fourier's Law of Heat Conduction

Fourier's Law quantitatively describes the rate of heat transfer through a material by stating that the rate is proportional to the cross-sectional area and the temperature difference, and inversely proportional to the distance over which the temperature difference exists. This law is fundamental in analyzing steady-state conduction scenarios.

Thermal Conductivity

Thermal conductivity is a material-specific constant that measures a material's ability to conduct heat. High thermal conductivity indicates that the material is efficient in transmitting heat, while low thermal conductivity suggests it acts more as an insulator.

Temperature Gradient

The temperature gradient refers to the rate of change of temperature per unit distance within a material. It is a crucial factor in determining the direction and magnitude of heat flow in conduction, as heat naturally flows from regions of higher temperature to regions of lower temperature.

Unit Conversion

Unit conversion is an essential step in solving physics problems, ensuring that measurements are expressed in a coherent set of units. For thermal conduction problems, converting measurements such as cross-sectional area from one unit (e.g., cm²) to another (e.g., m²) is vital for the correct application of equations.

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