What is the temperature (in ^oC) of the steel | vedclass

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Question

(B) In the steady state,the rate of heat flow through the steel rod must equal the rate of heat flow through the copper rod.Let $T$ be the temperature

Vedclass · Accepted Answer

$44.4$

Vedclass · Answer

(B) In the steady state,the rate of heat flow through the steel rod must equal the rate of heat flow through the copper rod.Let $T$ be the temperature of the junction.The rate of heat flow is given by $H = \frac{KA(T_H - T_L)}{L}$.For the steel rod $(1)$: $K_1 = 50.2 \; J s^{-1} m^{-1} K^{-1}$,$A_1 = 2A_2$,$L_1 = 0.15 \; m$,$T_H = 300^{\circ} C$,$T_L = T$.For the copper rod $(2)$: $K_2 = 385 \; J s^{-1} m^{-1} K^{-1}$,$A_2$,$L_2 = 0.10 \; m$,$T_H = T$,$T_L = 0^{\circ} C$.Equating the heat flow rates:$\frac{K_1 A_1 (300 - T)}{L_1} = \frac{K_2 A_2 (T - 0)}{L_2}$$\frac{50.2 	imes (2 A_2) 	imes (300 - T)}{0.15} = \frac{385 	imes A_2 	imes T}{0.10}$$\frac{100.4 	imes (300 - T)}{0.15} = \frac{385 	imes T}{0.10}$$669.33 	imes (300 - T) = 3850 	imes T$$200799 - 669.33 T = 3850 T$$4519.33 T = 200799$$T \approx 44.4^{\circ} C$.

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