Question

A cubical box of side $0.20m$ is constructed from $0.012m$ thick concrete panels of thermal conductivity $K=0.8W{m}^{-1}{K}^{-1}$. A $100W$ heater is sealed inside the box and switched on. The temperature of air outside the box is ${20}^{\circ }C$. After a long period of time, the air temperature inside the box will be close to

• A. ${20}^{\circ }C$
• B. ${22}^{\circ }C$
• C. ${24}^{\circ }C$
• D. ${26}^{\circ }C$

Answer 1

The correct option is D ${26}^{\circ }C$

Let the air temperature inside the box be $x^{o}C$

So,

$x-20=\frac{100\times 0.012}{6\times 0.2\times 0.2\times 0.8}\{H=\frac{△T}{\frac{l}{kA}}\Rightarrow △T=\frac{Hl}{kA}\}\Rightarrow x-20=6.25\Rightarrow x=26.25℃\Rightarrow x\approx 26℃$