If all solar energy reaching the planet could be converted to electricity with an efficiency of 50%, would it be sufficient to meet the world energy demand?

Question

BlackTom AI · Accepted Answer

Earth intercepts about 1.74 × 10^17 W of solar power at the top of the atmosphere, so even at 50% conversion efficiency there is vastly more energy than humanity currently uses.

1) Relevant knowledge points
- Solar constant (S) ≈ 1361 W/m^2 (power per unit area at Earth’s distance).
- Earth’s cross-sectional area = πR^2 (R = 6.371 × 10^6 m).
- Earth’s average albedo ≈ 0.30 (≈30% of incoming sunlight is reflected).
- World primary power demand ≈ 1.8 × 10^13 W (≈18 TW) (order-of-magnitude used for comparison).

2) Complete reasoning and 3) calculations (step-by-step)
- Cross-sectional area of Earth:
  R^2 = (6.371 × 10^6 m)^2 = 4.058 × 10^13 m^2
  A = πR^2 = π × 4.058 × 10^13 = 1.2755 × 10^14 m^2
- Total solar power intercepted:
  P_in = S × A = 1361 W/m^2 × 1.2755 × 10^14 m^2 = 1.736 × 10^17 W
- Power absorbed after reflection (1 − albedo = 0.70):
  P_absorbed = 0.70 × 1.736 × 10^17 W = 1.215 × 10^17 W
- If 50% of that absorbed sunlight could be converted to electricity:
  P_electric = 0.50 × 1.215 × 10^17 W = 6.075 × 10^16 W = 60,750 TW
- Compare to world demand (~18 TW):
  6.075 × 10^16 W / 1.8 × 10^13 W ≈ 3.4 × 10^3 → ~3,400 times larger

4) Why the correct answer is correct
Because even after realistic reflection losses and using only half of the remaining energy, the available electrical power (~6.1 × 10^16 W) exceeds global demand (~1.8 × 10^13 W) by several thousand times. That leaves a huge surplus — hence “Yes, with more to spare.”

5) Why the other choices are incorrect
- “Yes, just barely”: wrong because available power is thousands of times larger, not marginally larger.
- “No, not even close”: wrong because the available solar power greatly exceeds demand.
- “No, but it would satisfy a huge amount of it”: wrong because it wouldn’t just satisfy a huge amount; it would exceed total demand many times over.

6) Conclusion
Therefore the correct answer is: Yes, with more to spare — which matches the provided answer.

If all solar energy reaching the planet could be converted to electricity with an efficiency of 50%, would it be sufficient to meet the world energy demand?单项选择题

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