The thickness of a uniform rectangular metal | vedclass

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Question

(B) Given: Thickness $\Delta x = 5 ~mm = 5 	imes 10^{-3} ~m$, Area $A = 5 ~cm^2 = 5 	imes 10^{-4} ~m^2$, Temperature difference $\Delta T = 14^{\cir

Vedclass · Accepted Answer

$30 ~W ~m^{-1} ~K^{-1}$

Vedclass · Answer

(B) Given: Thickness $\Delta x = 5 ~mm = 5 	imes 10^{-3} ~m$, Area $A = 5 ~cm^2 = 5 	imes 10^{-4} ~m^2$, Temperature difference $\Delta T = 14^{\circ} C$, Heat flow rate $Q = 42 ~J/s = 42 ~W$.Using the formula for heat conduction in steady state:$Q = \frac{KA \Delta T}{\Delta x}$Rearranging for thermal conductivity $K$:$K = \frac{Q \Delta x}{A \Delta T}$Substituting the values:$K = \frac{42 	imes 5 	imes 10^{-3}}{5 	imes 10^{-4} 	imes 14}$$K = \frac{42 	imes 5 	imes 10^{-3}}{70 	imes 10^{-4}}$$K = \frac{210 	imes 10^{-3}}{70 	imes 10^{-4}} = 3 	imes 10^{1} = 30 ~W ~m^{-1} ~K^{-1}$.

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