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

Options

A. `4 "cal cm"^-2min.^(-1)`
B. `40 "cal cm"^-2min.^(-1)`
C. `4 J cm ^-2min.^(-1)`
D. `400 "cal cm "^-2min.^(-1)`

Answer

To solve the problem, we need to determine the amount of heat received from the sun per unit area per minute, given that 10 g of ice melts in 10 minutes when focused by a lens with a diameter of 5 cm.

### Step-by-Step Solution:

1. **Calculate the heat required to melt the ice:**
- The latent heat of fusion of ice is approximately 80 calories per gram.
- Therefore, the total heat (Q) required to melt 10 g of ice is:
\[ Q = \text{mass} \times \text{latent heat} = 10 \, \text{g} \times 80 \, \text{cal/g} = 800 \, \text{calories} \]

2. **Determine the heat received per minute:**
- Since 800 calories are used to melt the ice in 10 minutes, the heat received per minute (Q/min) is:
\[ Q/\text{min} = \frac{800 \, \text{cal}}{10 \, \text{min}} = 80 \, \text{cal/min} \]

3. **Calculate the area of the lens:**
- The diameter of the lens is given as 5 cm. Therefore, the radius (r) is:
\[ r = \frac{d}{2} = \frac{5 \, \text{cm}}{2} = 2.5 \, \text{cm} \]
- The area (A) of the lens is given by the formula for the area of a circle:
\[ A = \pi r^2 = \pi (2.5 \, \text{cm})^2 = \pi \times 6.25 \, \text{cm}^2 \approx 19.625 \, \text{cm}^2 \]

4. **Calculate the heat received per unit area:**
- To find the heat received per unit area per minute, we divide the heat received per minute by the area:
\[ \text{Heat per unit area} = \frac{Q/\text{min}}{A} = \frac{80 \, \text{cal/min}}{19.625 \, \text{cm}^2} \approx 4.08 \, \text{cal/cm}^2/\text{min} \]

### Final Answer:
The amount of heat received from the sun per unit area per minute is approximately **4.08 cal/cm²/min**.