Question

An ice box used for keeping eatables cool has a total wall area of $1m^2$ and a wall thickness of $5.0cm$. The thermal conductivity of the ice box is $K=0.01J/m^{o}C$. It is filled with ice along with eatables on a day when the temperature is ${30}^{o}C$. The latent heat of fusion of ice is $334\times {10}^{2}J/kg$. The amount of ice melted in one day is ($1$ day$=86,400$ seconds):

• A. $776g$
• B. $7760g$
• C. $11520g$
• D. $1552g$

Answer 1

The correct option is D $1552g$

Heat lost in $t$ second will be, $Q_1=KA\frac{\Delta \theta }{d}t=0.01\times 1\times \frac{30-0}{5\times {10}^{-2}}\times 86400Joule=518400Joule$

Suppose $m$ Kilogram ice got melted then $Q_2=mL=m\times 334000=Q_1=518400$

so $m=\frac{518400}{334000}=1.552kg=1552gm$