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^{

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 $Q = 42 \ J/s = 42 \ W$.The formula for heat conduction in steady state is $Q = \frac{K A \Delta T}{\Delta x}$.Rearranging for thermal conductivity $K$: $K = \frac{Q \Delta x}{A \Delta T}$.Substituting the values: $K = \frac{42 	imes 5 	imes 10^{-3}}{5 	imes 10^{-4} 	imes 14}$.Simplifying the expression: $K = \frac{42 	imes 10^{-3}}{10^{-4} 	imes 14} = \frac{3 	imes 10^{-3}}{10^{-4}} = 3 	imes 10 = 30 \ W \ m^{-1} \ K^{-1}$.

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