a 0.5 m^2 solar collector radiation from the sun and focuses it on 250g of water that is inially at 23 degrees . the average intensity of radiation arriving from the sun at this location is 550 Wm^-2. if you assume that this is collected with 100% efficiency. how much time is required for the collector to raise this temperatuer to boiling, at 100 degrees

To calculate the time required for the collector to raise the temperature of the water to boiling, we can follow these steps:

Step 1: Calculate the energy absorbed by the solar collector
The energy absorbed by the solar collector can be calculated using the formula:

Energy = intensity of radiation x area x time

Given:
Area of the solar collector (A) = 0.5 m^2
Intensity of radiation (I) = 550 W/m^2
Efficiency of the collector (η) = 100% = 1 (since we assume 100% efficiency)

Substituting the values into the formula, we have:

Energy = 550 W/m^2 x 0.5 m^2 x time
Energy = 275 W x time

Step 2: Calculate the heat energy required to raise the temperature of the water
The heat energy required to raise the temperature of the water can be calculated using the formula:

Heat Energy = mass x specific heat capacity x temperature change

Given:
Mass of water (m) = 250 g = 0.25 kg
Specific heat capacity of water (c) = 4.18 J/g°C (approximate value)
Initial temperature of the water (T1) = 23°C
Final temperature of the water (T2) = 100°C

Substituting the values into the formula, we have:

Heat Energy = 0.25 kg x 4.18 J/g°C x (100°C - 23°C)
Heat Energy = 0.25 kg x 4.18 J/g°C x 77°C
Heat Energy = 807.25 J

Step 3: Equate the absorbed energy to the heat energy required
Since the collector absorbs the radiation from the sun and converts it into heat energy, we can equate the energy absorbed by the collector to the heat energy required:

275 W x time = 807.25 J

Step 4: Solve for time
Rearranging the equation, we can solve for the time required:

time = 807.25 J / 275 W
time ≈ 2.93 seconds (approximately)

Therefore, it would take approximately 2.93 seconds for the collector to raise the temperature of the water from 23°C to 100°C.