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Question: A hot object of temperature \({{\text{T}}_{\text{1}}}\) is connected to a cold object of temperature...

A hot object of temperature T1{{\text{T}}_{\text{1}}} is connected to a cold object of temperature T2{{\text{T}}_2}. The object used to conduct heat has a length L and cross-sectional area A. The rate of heat-flow is:
A.A(T1 - T2)/ kL{\text{A}}\left( {{{\text{T}}_{\text{1}}}{\text{ - }}{{\text{T}}_{\text{2}}}} \right){\text{/ kL}}
B.k(T1 - T2)/ AL{\text{k}}\left( {{{\text{T}}_{\text{1}}}{\text{ - }}{{\text{T}}_{\text{2}}}} \right){\text{/ AL}}
C.kAL/(T1 - T2){\text{kAL/}}\left( {{{\text{T}}_{\text{1}}}{\text{ - }}{{\text{T}}_{\text{2}}}} \right)
D.kA(T1 - T2)/ L{\text{kA}}\left( {{{\text{T}}_{\text{1}}}{\text{ - }}{{\text{T}}_{\text{2}}}} \right){\text{/ L}}

Explanation

Solution

As per the law of thermal equilibrium, when two bodies of unequal temperature are kept in close contact with each other then, the hotter body transfers the heat to the colder body till the temperature of both the bodies are equal throughout.
Formula Used: ΔQΔt=−kAΔTΔx\dfrac{{{{\Delta Q}}}}{{{{\Delta t}}}}{{ = - kA}}\dfrac{{{{\Delta T}}}}{{{{\Delta x}}}},
Where, ΔQ{{\Delta Q}} is the net heat energy transfer, Δt{{\Delta t}} is the time taken, ΔT{{\Delta T}} is the difference in temperature between the cold and the hot ends, Δx{{\Delta x}} is the thickness of the heat conducting material, k is the thermal conductivity, and A is the surface area of the surface emitting heat.

Complete step by step answer:
As per the given question,
Temperature of the hot body =T1{{\text{T}}_{\text{1}}}
Temperature of the cold body = T2{{\text{T}}_2}
The length of the object = L and the cross-sectional area = A.
Therefore the rate of flow of heat is equal to the amount of hat transferred per unit time in some material, usually measured in watt (joules per second).
As per the formula for the rate of flow of heat,
Putting the values given in the above equation, we get that the rate of heat flow is,
Qt = kA(T1 - T2)L\dfrac{{\text{Q}}}{{\text{t}}}{\text{ = kA}}\dfrac{{\left( {{{\text{T}}_{\text{1}}}{\text{ - }}{{\text{T}}_{\text{2}}}} \right)}}{{\text{L}}}

Hence, the correct answer is option D.

Note:
The equation of the rate of flow of heat is given by the Fourier’s Law of heat conduction. Heat should not be consumed with the thermal energy that is stored inside the body, instead it is the flow of the thermal energy, driven by the non-thermal equilibrium of the bodies among which heat is transferred.