Question

A thermocol box has a total wall area (including the lid) of $1.0m^2$ and wall thickness of $3cm$. It is filled with ice at $0^{o}C$. If the average temperature outside the box is ${30}^{o}C$ throughout the day, the amount of ice that melts in one day is
(Use $K_{thermocol}=0.03W/mK,L_{fusion\left(ice\right)}=3.00\times {10}^{5}J/kg$

• A. $1kg$
• B. $2.88kg$
• C. $25.92kg$
• D. $8.64kg$

Answer 1

The correct option is D $8.64kg$

Given : $A=I{m}^2$
$L=3\times {10}^{5}J/kg$
$l=3cm=3\times {10}^{-2}m$
$t=24\times 60\times 60s$
$\Delta \theta =30-0={30}^{o}C$
Using $\frac{Q}{t}=\frac{KA}{l}\Delta \theta$
or $\frac{mL}{t}=\frac{KA}{l}\Delta \theta$
Putting the values, $\frac{m\times 3\times {10}^5}{24\times 60\times 60}=\frac{0.03\times 1}{3\times {10}^{-2}}\times 30$
$⟹m=8.641kg$