The maximum efficiency of hydrogen fuel cell is

Correct option is C

Introduction
· A hydrogen fuel cell is an electrochemical device that converts the chemical energy of hydrogen and oxygen directly into electricity, with water and heat as the only byproducts.
· Unlike heat engines (like internal combustion engines), fuel cells are not limited by the Carnot cycle because they do not involve the intermediate step of converting thermal energy into mechanical work.
· The efficiency of a fuel cell is defined by the ratio of the electrical energy produced to the total energy available in the fuel (enthalpy).

Information Booster
· The correct answer is 0.83 (or 83%), which represents the maximum theoretical efficiency of a hydrogen-oxygen fuel cell at standard operating conditions ($$25^\circ\text{C} and 1 \text{ atm}$$​
· This theoretical efficiency is determined by the ratio of the Gibbs free energy ($$\Delta G$$​) to the Enthalpy change $$(\Delta H$$​) for the reaction: $$H_2 + \frac{1}{2}O_2 \rightarrow H_2O$$​
· Mathematically, $$\text{Efficiency} = \frac{\Delta G}{\Delta H}. Since \Delta G$$​ represents the "useful" work and $$\Delta H$$​ is the total heating value, the remaining 17% of energy is lost as heat due to the entropy change of the reaction.
· In practical applications, real-world fuel cells operate at efficiencies between 40% and 60% due to internal resistances (activation, ohmic, and concentration losses).
· However, if the byproduct heat is captured and used (combined heat and power or CHP), the overall system efficiency can exceed 80%.

Additional Knowledge
· 0.96 and 0.92 are values that exceed the thermodynamic limits of a standard hydrogen fuel cell at room temperature; while efficiency can theoretically increase as temperature decreases, these values are not standard for the $$H_2/O_2$$​reaction.
· 0.72 is a realistic efficiency target for some advanced high-temperature fuel cells (like Solid Oxide Fuel Cells) when considering their electrical output, but it is not the maximum theoretical limit.
· The "Lower Heating Value" (LHV) vs "Higher Heating Value" (HHV) of hydrogen can lead to different efficiency calculations; the 0.83 value is typically referenced against the HHV.
· Fuel cells are significantly more efficient than gasoline engines, which typically operate at roughly 20-30% efficiency because they must lose a large portion of energy as heat to the environment to satisfy the laws of thermodynamics.