Question

Consider a gallon water insulated to prevent any significant heat loss and steady at 21ºC. Estimate the radiant power of the sun using the following information. If a 600 cm2 magnifying lens is used to focus the sun’s light on the water, it takes about 4 hours and 15 minutes to make the water boil

Answer 1

To estimate the radiant power of the sun, we calculate the initial rate of heating of water using the given information and the formula for power absorbed. The initial rate of heating is 0.251 °C/s.

Step-by-step explanation:

To estimate the radiant power of the sun, we need to calculate the initial rate of heating of the water using the given information. The intensity of sunlight is 1.00 kW/m², and a circular lens with a diameter of 0.200 m focuses the light onto the water. Assuming the sunlight is unpolarized and 80.0% absorbed, we can calculate the initial rate of heating of the water in °C/s.

To calculate the initial rate of heating, we need to consider the power absorbed by the water. The power absorbed can be calculated using the formula:

Power Absorbed = Intensity of Sunlight × Area of Lens × Absorption Efficiency = (1.00 kW/m²) × (π × (0.100 m)²) × 0.80

Substituting the values into the formula, we get:

Power Absorbed = 0.251 kJ/s

Therefore, the initial rate of heating of the water is 0.251 °C/s.