Question

A cubical box is used to keep drinks cold in a bus. Surface area of each face of cubical box is $0.8$ $m^2$ and each wall has thickness $2$ cm. It is filled with ice and water which remains at $0^{0}C$. Temperature at outside each wall is ${30}^{0}C$, then
(Thermal conductivity of material of box = $1\times {10}^{-2}$ W/m-k and latent heat of fusion of ice = $3.2\times {10}^5$ J/kg)

• A. total heat current in the box is 60 J/s
• B. total heat current in the box is 72 J/s
• C. mass of ice melted in 1 hour is 810 gm
• D. mass of ice melted in 1 hour is 690 gm

Answer 1

Answer: (B), (C)

total heat current in the box is 72 J/s
mass of ice melted in 1 hour is 810 gm

Let H be the rate of transfer of heat.
$H=KA\frac{(T_2-T_1)}{x}$ where $T_2-T_1$ is the temp diff between the outside and inside the wall of the box and x is the thickness of the wall, K is the thermal conductivity and A is the surface area of the wall.
Since there are 6 faces of the cubical box,
$H_{total}=6H=6\times 0.01\times 0.8\times (30-0)\times \frac{1}{0.02}=72J/s$
Now, we can calculate how much of ice melts in one hour.
Amount of heat conducted in one hour is $72\times 3600J$
Amount of ice melted in one hour $m=\frac{72\times 3600}{3.2\times {10}^5}=0.81kg=810gm$