Two rods of same length and cross-section are | vedclass

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(C) At steady state,the rate of heat flow $(H)$ through both rods must be equal.The formula for the rate of heat flow is $H = \frac{KA(\Delta T)}{l}$.

Vedclass · Accepted Answer

$\frac{K_1 	heta_1 + K_2 	heta_2}{K_1 + K_2}$

Vedclass · Answer

(C) At steady state,the rate of heat flow $(H)$ through both rods must be equal.The formula for the rate of heat flow is $H = \frac{KA(\Delta T)}{l}$.Let $	heta$ be the temperature of the common junction. Since the rods are joined in series,the heat current flowing through the first rod equals the heat current flowing through the second rod:$\frac{K_1 A (	heta_1 - 	heta)}{l} = \frac{K_2 A (	heta - 	heta_2)}{l}$Since the lengths $(l)$ and cross-sectional areas $(A)$ are the same,they cancel out:$K_1(	heta_1 - 	heta) = K_2(	heta - 	heta_2)$$K_1 	heta_1 - K_1 	heta = K_2 	heta - K_2 	heta_2$$K_1 	heta_1 + K_2 	heta_2 = 	heta(K_1 + K_2)$$	heta = \frac{K_1 	heta_1 + K_2 	heta_2}{K_1 + K_2}$

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