Question

A cube of side 10cm is filled with ice of density 0.9gm/cc. Thickness of the walls of the cube is 1mm and thermal conductivity of the material of cube is 0.01CGS units. If the cube is placed in steam bath maintained at temperature of 100^oC, then the time in which ice completely melts?(latent heat of fusion of ice = 80 cal/gm)

Answer 1

As we know, mass of ice cube is m = pV = $0.9\times {10}^3=900gm$

total heat absorbed = mL= $7.2\times {10}^{3}cal$

$\theta =\frac{Q}{t}=\frac{KA\Delta T}{t}$

$\theta =\frac{(6\times 0.01\times 100\times 100)}{0.1}=6000$

$\theta =6000$

cal/sec

time taken to melt ice = $\frac{Q}{\theta }$ =$\frac{(72\times {10}^3)}{6000}=12sec$