Energy Science (XE-I): Conversion, Resources, and System Limits
Energy Science (XE-I) tests quantitative reasoning about energy resources, conversion chains, storage, and system constraints. Questions commonly combine thermodynamics, power cycles, solar and wind resources, biofuels, fuel cells, and efficiency/emissions accounting. The section rewards clear reference choices-per square metre, per kilogram, per year, or per kWh-and careful conversion between power (kW) and energy (kWh).
Core rules and concepts
- Apply the first law to conversion devices; use the second law to set quality limits and identify irreversibility.
- Distinguish rated power from delivered energy: capacity factor = actual annual energy / (rated power × 8760 h).
- Solar PV output depends on irradiance, area, efficiency, temperature derating, and inverter losses; name the reference condition when quoting efficiency.
- Wind power available in the rotor sweep is P = ½ρAv³. The Betz limit, 16/27 ≈ 0.593, is the maximum fraction extractable by an ideal rotor; real power coefficient C_p is lower.
- For storage, report round-trip efficiency, usable depth of discharge, and energy/power density separately.
- Emissions intensity in gCO₂/kWh must state system boundaries and whether it is lifecycle or direct.
Worked example
A wind turbine has rotor diameter 50 m, air density 1.2 kg/m³, wind speed 10 m/s, C_p = 0.40, and capacity factor 0.30. Radius r = 25 m, so A = πr² = 1963.5 m². Available wind power P_wind = ½ρAv³ = 0.5 × 1.2 × 1963.5 × 1000 = 1.178 MW. The Betz maximum is 0.593 × 1.178 = 0.699 MW. Actual electrical output is C_p P_wind = 0.40 × 1.178 = 0.471 MW. Annual energy = 0.471 MW × 8760 h × 0.30 = 1238 MWh.
Traps that cost marks
- Using diameter as radius or omitting the cube on wind speed.
- Treating the Betz limit as an actual efficiency rather than an ideal upper bound.
- Mixing MW with MWh, or using 365 days in place of 8760 hours.
- Quoting PV efficiency at STC as if it were field output without temperature and irradiance corrections.
- Comparing storage technologies on energy density alone while ignoring power density and round-trip efficiency.