Question

The Earth is 1.49×10¹¹ meters from the sun. The solar radiation at the top of the Earth's atmosphere is 1340 W/m² a. answer. b. What is the average total power output of the Sun. c. c. of the Earth's atmosphere.

Answer 1

The power per square meter reaching Earth from the Sun is approximately 1,360 W/m². Part of this is absorbed and reflected by the atmosphere, allowing a maximum of 1.30 kW/m² to reach the surface. An area of solar collectors is calculated by taking into account the power output of a power plant and the conversion efficiency of the collectors.

Step-by-step explanation:

To calculate the power per square meter reaching Earth's upper atmosphere from the Sun, we use the solar constant which is approximately 1,360 W/m². This value represents the solar radiation that arrives at the top of Earth's atmosphere. The total power output of the Sun (P_out) can be represented by the formula 4πR²σT⁴, but for simplicity, we can use the provided value of 4.00 × 10²⁶ W.

To address part (b) of the question, we use the information that a maximum of 1.30 kW/m² reaches Earth's surface after being absorbed and reflected by the atmosphere, and the solar energy collectors have an average conversion efficiency of 2.00%. To provide the output of a 750 MW power plant, we first convert 750 MW to W (750 × 10¶ W), and then calculate the area of the solar energy collectors required as follows:

Area = Power Plant Output / (Intensity × Conversion Efficiency)

Area = (750 × 10¶ W) / (1.30 × 10³ W/m² × 0.02)

The result will give us the area in m², which can be converted to km² by dividing by 10⁶.

Answer 2

To calculate the power per square meter reaching Earth's upper atmosphere from the Sun, divide the power output of the Sun by the area of the Earth's surface.

Step-by-step explanation:

The power per square meter reaching Earth's upper atmosphere from the Sun can be calculated by dividing the power output of the Sun by the area of the Earth's surface. In this case, the power output of the Sun is given as 4.00 × 10^26 W and the radius of the Earth is approximately 6,378 km. Using these values, we can calculate the power per square meter reaching Earth's upper atmosphere as follows:

Power per square meter = Power output of the Sun / Area of the Earth's surface

Power per square meter = 4.00 × 10^26 W / (4π × (6,378,000 m)^2)

After calculating the above expression, we can find the power per square meter reaching Earth's upper atmosphere.

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