It takes 20 minutes to melt 10 g of ice, when rays from the 'sun are focussed by a lens of diam

step 1 Hello students in this question we have given that it take time t equals to 20 minutes to melt m

It takes 20 minutes to melt 10 g of ice, when rays from the...

It takes 20 minutes to melt $10 \mathrm{~g}$ of ice, when rays from the 'sun are focussed by a lens of diameter $5 \mathrm{~cm}$ on to a block of ice. The heat received from the sun on $1 \mathrm{~cm}^{2}$ per minute is : (Given: $L=80 \mathrm{k} \mathrm{cal} / \mathrm{kg}$ ) (a) $R=2.04 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}$ (b) $R=3.04 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}$ (c) $R=0.204 \mathrm{cal} / \mathrm{cm}^{2}-\min$ (d) $R=204 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}$

It takes 20 minutes to melt $10 \mathrm{~g}$ of ice, when rays from the 'sun are focussed by a lens of diameter $5 \mathrm{~cm}$ on to a block of ice. The heat received from the sun on $1 \mathrm{~cm}^{2}$ per minute is : (Given: $L=80 \mathrm{k} \mathrm{cal} / \mathrm{kg}$ )
(a) $R=2.04 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}$
(b) $R=3.04 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}$
(c) $R=0.204 \mathrm{cal} / \mathrm{cm}^{2}-\min$ (d) $R=204 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}$

Key Concepts

Latent Heat of Fusion

Latent heat refers to the amount of energy per unit mass required to change the state of a substance without changing its temperature. In the context of melting, the latent heat of fusion is the energy needed to convert ice to water, and understanding this concept is fundamental to calculating the energy absorbed during the phase change.

Energy Balance in Phase Change

This concept involves equating the energy supplied (or absorbed) to the material with the energy required for a phase change, computed as the mass multiplied by the latent heat. It is essential in problems where one needs to estimate the energy transfer involved in melting or freezing processes.

Solar Irradiance (Energy Flux)

Solar irradiance, or energy flux, is the measure of solar energy received per unit area per unit time. This concept is crucial for determining how much energy a surface, such as an ice block, receives, and it is often expressed in terms of cal/cm²-min or similar units.

Lens Area Calculation

Calculating the area of a circular lens involves using the geometric formula for the area of a circle. This step is important when determining the total amount of energy collected from the sun since the energy incident on the lens is directly proportional to its area.

Optical Concentration

Optical concentration refers to using lenses or mirrors to focus solar radiation onto a specific area, thereby increasing the energy flux on that area. This concept underlies many solar energy applications and is illustrated by focusing sunlight to melt ice in the given problem.

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