A wall made of wood \(4.0 cm\) thick has area of \(48.0 m ^{2}\). If the temperature inside is \(25^{\circ} C\) and the temperature outside is \(14^{\circ} C\), at what rate is thermal energy transported by conduction? [Thermal conductivity \(k\) for wood \(=0.08 Wm ^{-1} k ^{-1}\) ].
A. \(82 W\) B. \(210 W\) C. \(690 W\) D. \(1100 W\)
Correct Answer: D
Explanation
Analysisorrelating equation: Fourier's law of heat of conduction The rate of energy transfer by conduction through a material is given by $$ P=K A \frac{\left(T_{h}-T_{c}\right)}{L} $$ where \(K=\) thermal conductivity \(A=\) Area \(=48.0 m ^{2}\) \(T_{h}=\) hotter temperature \(=25^{\circ} C\) \(T_{c}=\) colder temperature \(=14^{\circ} C\) \(L=\) thickness of the material \(=4 cm =0.04 m\) \(\Rightarrow 0.08 \times \frac{48(25-14)}{0.04}\) \(=\underline{42.24}=1056 \approx 1100 W\)
