Question

The rays of sun are focussed on a piece of ice through a lens of diameter 5 cm, as a result of which 10 g ice melts in 10 min. The amount of heat received from sun, per unit area per minute is :

• A. \(4 \, \text{cal/cm}^2 \text{ min}\)
• B. \(40 \, \text{cal/cm}^2 \text{ min}\)
• C. \(4 \, \text{J/m}^2 \text{ min}\)
• D. \(400 \, \text{cal/cm}^2 \text{ min}\)

Hint:

Always use latent heat for phase change problems: \(Q = mL\).

Answer 1

The Correct Option is A

Concept: Heat required to melt ice: \[ Q = mL \] where \(L = 80 \, \text{cal/g}\)

Step 1: Heat required.
\[ Q = 10 \times 80 = 800 \, \text{cal} \]

Step 2: Area of lens.
\[ A = \pi r^2 = \pi (2.5)^2 = 20 \, \text{cm}^2 \]

Step 3: Heat per unit area per minute.
\[ \frac{Q}{A \cdot t} = \frac{800}{20 \times 10} = 4 \, \text{cal/cm}^2 \text{ min} \]