Question

The interior dimensions of a cooler box are 45cm x 35cm x 30cm. Each wall is 3.75cm thick

and is made from plastic whose thermal conductivity is 0.032W/m.K. If the box is to

maintain an inside temperature of 0oC when the outside temperature is 30oC, how much ice

will melt inside the box each hour?

Answer 1

$S=2(ab+ac+bc)=0.795~m^2,$

$q=\frac Q{TS}=\frac{Lm}{TS}=\frac{\lambda(t_2-t_1)}d,\implies$

$\frac mT=\frac{\lambda S(t_2-t_1)}{Ld},$

$\frac mT=\frac{0.032\cdot 0.795\cdot(30-0)}{340000\cdot 0.0375}=6\cdot 10^{-6}~\frac{kg}s,$

$(\frac mT)_{hr}=\frac mT\cdot 3600=215~\frac g{hr}.$