Two rods (one semi-circular and other straigh | vedclass

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Question

(A) The rate of heat flow through a rod is given by the formula: $\frac{dQ}{dt} = \frac{KA \Delta 	heta}{l}$.Here,$K$ is the thermal conductivity,$A$

Vedclass · Accepted Answer

$2 : \pi$

Vedclass · Answer

(A) The rate of heat flow through a rod is given by the formula: $\frac{dQ}{dt} = \frac{KA \Delta 	heta}{l}$.Here,$K$ is the thermal conductivity,$A$ is the cross-sectional area,$\Delta 	heta$ is the temperature difference,and $l$ is the length of the rod.Since both rods are made of the same material,$K$ is the same for both.They have the same cross-sectional area $A$,and the points $A$ and $B$ are maintained at the same temperature difference $\Delta 	heta$ for both paths.Therefore,the rate of heat flow is inversely proportional to the length of the rod: $\frac{dQ}{dt} \propto \frac{1}{l}$.The length of the straight rod is $l_{straight} = 2r$,where $r$ is the radius.The length of the semi-circular rod is $l_{semi} = \pi r$.Thus,the ratio of heat transferred is:$\frac{(dQ/dt)_{semi}}{(dQ/dt)_{straight}} = \frac{l_{straight}}{l_{semi}} = \frac{2r}{\pi r} = \frac{2}{\pi}$.

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