Two rods of same length and material transfer | vedclass

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(B) Let the length of each rod be $\ell$,area of cross-section be $A$,and thermal conductivity be $K$. The heat transferred is given by $Q = \frac{KA

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$3$

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(B) Let the length of each rod be $\ell$,area of cross-section be $A$,and thermal conductivity be $K$. The heat transferred is given by $Q = \frac{KA \Delta T}{L_{eq}} 	imes t$.Case $1$: Series combination (end to end).The equivalent length is $L_{eq} = \ell + \ell = 2\ell$. The equivalent area is $A$.$Q = \frac{KA \Delta T}{2\ell} 	imes 12 \quad \dots (1)$Case $2$: Parallel combination (along their lengths).The equivalent length is $L_{eq} = \ell$. The equivalent area is $A_{eq} = A + A = 2A$.$Q = \frac{K(2A) \Delta T}{\ell} 	imes t \quad \dots (2)$Since the heat $Q$ and temperature difference $\Delta T$ are the same in both cases,we equate $(1)$ and $(2)$:$\frac{KA \Delta T}{2\ell} 	imes 12 = \frac{2KA \Delta T}{\ell} 	imes t$$\frac{12}{2} = 2t$$6 = 2t$$t = 3 \ s$.

Two rods of same length and material transfer a given amount of heat in $12 \ s$,when they are joined end to end. But when they are joined along their lengths (parallel combination),then they will transfer the same amount of heat under the same conditions in time $t = \dots \ s$.

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