Solar heating takes advantage of solar collectors such as the type shown in the figure . During daylight hours, the average intensity of solar radiation at the top of the atmosphere is about 1400 W/m^2. About 50% of this radiation reaches the Earth during daylight hours. (The rest is reflected, scattered, absorbed, and so on.) How much heat energy would be received, on average, by the cylindrical collector shown in the figure during 10 h of daylight?
Length of 4.0m
Radius of 0.5m
To find the heat energy received by the cylindrical collector during 10 hours of daylight, we need to calculate the area of the collector and then multiply it by the average intensity of solar radiation.
1. Calculate the area of the cylindrical collector:
The area of the curved surface of a cylinder is given by the formula:
A = 2πrh, where A is the surface area, π is a constant (approximately 3.14), r is the radius, and h is the height (proper length in this case).
In this case, the length of the cylindrical collector is given as 4.0m, and the radius is given as 0.5m. So, plugging in the values:
A = 2π(0.5)(4.0) = 4π square meters
2. Calculate the average heat energy received by the collector during 10 hours of daylight:
The average intensity of solar radiation at the top of the atmosphere is given as 1400 W/m^2. However, only 50% of this radiation reaches the Earth, so we need to consider this.
The total heat energy received by the collector can be calculated using the formula:
Heat energy = Intensity of solar radiation x Area x Time
The intensity of solar radiation reaching the Earth during daylight hours is 1400 W/m^2 * 0.50 = 700 W/m^2.
Now, we can calculate the heat energy received by the collector during 10 hours of daylight:
Heat energy = 700 W/m^2 * 4π square meters * 10 hours
To get the final answer, you need to calculate this expression.