Questions: Energy from the Sun arrives at the top of the Earth's atmosphere with an intensity of 1.36 kW/m^2. How long t does it take for 1.75 × 10^9 J to arrive on an area of 4.75 m^2. t= S

Solution Steps

We need to find the time \( t \) it takes for a certain amount of energy to arrive on a given area, given the intensity of solar energy at the top of the Earth's atmosphere.

The intensity \( I \) of solar energy is given by: \[ I = \frac{P}{A} \] where \( P \) is the power and \( A \) is the area. We can rearrange this to find the power: \[ P = I \times A \]

Given:

• Intensity \( I = 1.36 \, \text{kW/m}^2 = 1360 \, \text{W/m}^2 \)
• Area \( A = 4.75 \, \text{m}^2 \)

Substitute these values into the formula for power: \[ P = 1360 \, \text{W/m}^2 \times 4.75 \, \text{m}^2 = 6460 \, \text{W} \]

The energy \( E \) received over time \( t \) is given by: \[ E = P \times t \] Rearrange to solve for time \( t \): \[ t = \frac{E}{P} \]

Given:

• Energy \( E = 1.75 \times 10^9 \, \text{J} \)
• Power \( P = 6460 \, \text{W} \)

Substitute these values into the formula for time: \[ t = \frac{1.75 \times 10^9 \, \text{J}}{6460 \, \text{W}} \approx 270904.0186 \, \text{s} \]

Final Answer