Which of the following circular rods, (given radius r and length l ) each made of the same material and whose ends are maintained at the same temperature will conduct most heat?

Step-by-step solution

Heat conduction through a rod is rate of change of heat ( Q t ) . H= Q t =K A ( T₁-T₂ l ) H r^2 l ...(i) (a) When aligned r & =2 r₀, l=2 l₀ H & (2 r₀ )^2 2l₀ H 2 r₀^2 l₀ aligned (b) When aligned r & =2 r₀, l=l₀ H & (2 r₀ )^2 l₀ H 4 r₀^2 l₀ aligned (c) When gathered r=r₀, l=l₀ H r₀^2 l₀ gathered (d) When aligned r & =r₀, l=2 l₀ H & r₀^2 2 l₀ aligned It is obvious that heat conduction will be more in case (b).