Scenario...

Assumed stable world population: 1.0 × 1010
Per-capita energy use in the United States: 300 GJ/yr [1]
Energy supply goal: 3.0 × 1021 J/yr (as electricity)

Fission

Uranium, reasonably assured resources (RAR) at $130/kgU: 3.7 × 109 kg [2]
Uranium, natural flow to the sea: 3.2 × 107 kg/yr [3]
Energy yield (electric) of natural uranium in commercial LWRs: 2.7 × 1011 J/kg [4]
...in advanced reactors: factor of 50 higher [5][6]

Solar, theoretical

A generous estimate for insolation is 7.2 × 109 J/m2*yr. Let's say PV gets to 68% efficiency. Assuming 15% grid & storage loss (grid < 10%, pumped hydro storage ~ 20%) we need 720,000 km2 to supply the desired 3.0 × 1021 J/yr. Compare to 1,500,000 km2 of global urban development.

Solar, practical

Sanyo's HIT Power 215N solar panel will make 2.6 × 1010 J in its 20-year lifetime† at the above insolation, net its 10% embodied energy. It weighs 16 kg, so it delivers 1.6 × 109 J/kg as a fuel – two orders of magnitude less than uranium today. It costs $900, or 2.8 × 107 J/$. Uranium at $130/kg gives 2.1 × 109 J/$.

† Panel is 1.26 m2, ~ 16% efficient at 46°C. Manufacturer guarantees efficiency for 20 years; useful service life may be longer.

References

  1. Data for 2013, World Bank 2016
  2. Data for 2013, Red Book 2014, Table 1.1
  3. Bernard Cohen 1983, Breeder reactors: A renewable energy source
  4. Barry Brook 2011
  5. Transatomic Power white paper 1.0.1, pg 25, harmonized to [4]
  6. TerraPower 2016