Both pathways start from the same H2 + O2 → H2O reaction and release the same 286 kJ/mol of chemical energy. The difference is how that energy is extracted.
Combustion (left) burns H2 and O2 directly — an uncontrolled reaction whose energy comes out purely as heat. That heat can only become useful work by running a heat engine between a hot reservoir (Th) and a cold one (Tc), and no heat engine, however well built, can beat the Carnot ceiling η = 1 − Tc/Th. Everything above that line is thermodynamically forbidden, and real engines fall well short of even that ceiling.
PEM fuel cell (right) never lets H2 and O2 meet directly. At the anode, a catalyst splits H2 into protons (which cross the membrane) and electrons (which are forced through an external wire to do electrical work) before recombining with O2 at the cathode to form water. Because the energy leaves as electricity from the start, it is not bound by the Carnot limit — its ceiling is set instead by the cell voltage relative to hydrogen's thermoneutral voltage (1.48 V).
η_carnot = 1 − Tc/Th (combustion ceiling)
η_engine = η_carnot × 0.55 (real irreversibilities)
η_fuelcell = V_cell / 1.48 V (no Carnot limit)
- Fuel supply — H2 flow feeding both pathways identically, for a fair side-by-side comparison.
- Th / Tc — raising Th or lowering Tc raises the combustion ceiling, but it stays capped well under 100%.
- External load — drawing more current from the fuel cell pulls its voltage down (activation + ohmic + concentration losses), which is why efficiency is highest at light load.