A body of length 1 m having cross-sectional area 0.75 m^2 has thermal conductivity 6000 J / s

step 1 Hello students in this question we have a body of length L equals to one meter having cross -sec

A body of length 1 m having cross-sectional area 0.75 m^2...

A body of length $1 \mathrm{~m}$ having cross-sectional area $0.75 \mathrm{~m}^{2}$ has thermal conductivity $6000 \mathrm{~J} / \mathrm{s}$ then the temperature difference if $\mathrm{K}=200 \mathrm{Jm}^{-1} \mathrm{~K}^{-1}$, will be : (a) $20^{\circ} \mathrm{C}$ (b) $40^{\circ} \mathrm{C}$ (c) $80^{\circ} \mathrm{C}$ (d) $100^{\circ} \mathrm{C}$

A body of length $1 \mathrm{~m}$ having cross-sectional area $0.75 \mathrm{~m}^{2}$ has thermal conductivity $6000 \mathrm{~J} / \mathrm{s}$ then the temperature difference if $\mathrm{K}=200 \mathrm{Jm}^{-1} \mathrm{~K}^{-1}$, will be :
(a) $20^{\circ} \mathrm{C}$
(b) $40^{\circ} \mathrm{C}$
(c) $80^{\circ} \mathrm{C}$
(d) $100^{\circ} \mathrm{C}$

Key Concepts

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 temperatures and the area through which the heat flows. It is commonly expressed as Q/t = (k · A · ?T) / L, where Q/t is the rate of heat transfer, k is the thermal conductivity, A is the cross-sectional area, ?T is the temperature difference, and L is the length of the material. This concept is fundamental in understanding how heat moves through solids under steady conditions.

Thermal Conductivity

Thermal conductivity is a material property that indicates a material's ability to conduct heat. A higher thermal conductivity means that the material allows heat to pass through it more easily, while a lower value indicates that the material is more resistant to heat flow. It is critical in calculations involving heat transfer, as it directly affects the rate at which energy is transmitted through a substance.

Steady-State Heat Transfer

Steady-state heat transfer refers to a condition where the temperature distribution in a material does not change with time, meaning the amount of heat entering any region equals the amount of heat leaving it. This concept simplifies the analysis by allowing the use of constant values in the conduction equation, thereby enabling straightforward calculation of temperature differences when other variables such as heat flow rate, material dimensions, and thermal conductivity are known.

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