Question

A hollow metal cube, with side $0.5$m and wall thickness $5\times 10$${}^{-3}$m is filled with ice. It is immersed in water tank maintained at $100$${}^o$C. Calculate the amount of ice melted in $335$ sec. (Conductivity of metal $=0.5W{m}^{-1}{K}^{-1},$ Latent heat of fusion of ice $=335$x${10}^{3}Jk{g}^{-1}$)

• A. 15kg
• B. 15g
• C. 1.5kg
• D. 1.5g

Answer 1

The correct option is A 15kg

Let the mass of ice melted is $m$.
$Q=mL$ where $L$ is the latent heat of fusion of ice.
Heat conducted across six faces of the cube is$\frac{KA({\theta }_1-{\theta }_2)t}{x}$
where x is the thickness of the wall and A is the area of each wall
$\therefore mL=\frac{KA({\theta }_1-{\theta }_2)t}{x}$ .....(1)
Given,
$K=0.5$
$L=335\ast {10}^3$
${\theta }_1=0^{0}C$
${\theta }_2={100}^{0}C$
$t=335s$
$A=6\ast (0.5{)}^2$
Substituting the values in (1)
$m=\frac{0.5(6\ast .25)\ast (100-0)\ast 335}{335\ast {10}^3\ast 5\ast {10}^{-3}}=15kg$