Energy Science (XE-I) - new sectional paper within XE
What XE-I tests
Energy Science (XE-I) is a specialised sectional paper inside XE. It examines the physical limits and practical metrics of energy conversion: thermodynamic availability, solar and wind resources, biomass and hydro, nuclear fission, storage, and the economics of delivered energy. Numerical questions dominate, so unit discipline and correct limiting efficiencies matter.
Core rules and concepts
- Carnot efficiency for a heat engine is η=1−T_c/T_h with absolute temperatures; no real cycle between the same reservoirs can exceed it.
- Exergy (availability) of a stream is (H−H₀)−T₀(S−S₀); irreversibility destroys exergy, not energy.
- Wind power through a rotor area A is P=0.5ρAv³; the Betz limit is 16/27≈0.593 of the wind's kinetic power.
- The solar constant is about 1361 W/m² at the top of the atmosphere; PV ratings use STC (1000 W/m², AM1.5, 25 °C).
- Hydropower is P=ρgQHη; nuclear fission releases about 200 MeV per U-235 fission.
- Storage is characterised by energy density, power density, round-trip efficiency and depth of discharge.
- LCOE divides lifetime costs by lifetime energy; capacity factor is actual output divided by rated output over the same period.
Worked example
An 80 m diameter wind turbine operates at v=10 m/s in air of density 1.225 kg/m³ with Cp=0.45. Rotor area A=π(40)²≈5027 m². P=0.5×1.225×5027×10³×0.45≈1.39 MW. The Betz ceiling at this wind speed would be 0.593×3.08 MW≈1.83 MW, so the assumed Cp is physically admissible. With a 35% capacity factor, annual energy is 1.39 MW×8760 h×0.35≈4.25 GWh.
Traps
- Reporting kW as kWh; power and energy differ by time.
- Multiplying rated capacity by 8760 h and calling it generation; apply the capacity factor.
- Using Cp>0.593, which violates the Betz limit.
- Applying Carnot efficiency to a heat pump; use COP.
- Mixing lower and higher heating values for a fuel.
- Scaling wind power with v² (that is force) instead of v³.