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Sun rays are allowed to fall on a lens of diameter 20 cm. They are then brought to focus on a calorimeter containing 20 g of ice. If the absorption by the lens is negligible, the time required to melt all the ice is (Take, solar constant = 1.9 cal $\min^{- 1}$ ${cm}^{- 2}$ and L = 80 cal $g^{- 1}$ )

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3.2 min

7.2 min

2.7 min

answer is D.

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Detailed Solution

Heat required to melt whole ice is

$Q = m L = 20 \times 80 = 1600 cal$

Energy incident per minute is

$P = 1.9 \times \frac{π}{4} \times d^{2} = 1.9 \times \frac{π}{4} \times (20)^{2} = 597 cal \min^{- 1}$

Therefore, time required to melt whole ice is $t = \frac{Q}{P} \approx 2.7 \min$

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