A cubical vessel of side $10 c m$ is filled with ice at $0^{o} C$ and is immersed in water bath as $100^{o} C$ . If thickness of walls of vessel is $0.2 c m$ and conductivity is $0.02 C G S u n i t s$ , then time in which all the ice melts is (Density of ice= $0.9 g m / c c$ )

6 s e c

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9 s e c

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12 s e c

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15 s e c

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Solution

The correct option is A $6 s e c$
we have formula,

$\frac{Δ Q}{t} = K A (θ_{1} - θ_{2}) l$

Area on one side of cube $= 10^{2} = 100 c m^{2}$

$\frac{Q}{t} = \frac{1 \times 100 \times (100 - 0)}{0.2}$

$Q p r o v i d e d = 50000 J / s$

density=mass / volume

mass=desity*volume $= 0.91000 k g / c m$

Latent heat of fusion for ice is $L = 3.36 \times 10^{5} J / k g$

Therefore heat required to melt ice $Q_{L} = m L = 0.9 \times 3.36 \times 10^{5} = 302400 J$

So time taken for ice to melt is $t = \frac{Q_{L}}{Q p r o v i d e d} = \frac{302400}{50000} = 6 s e c o n d s$

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