Fuel Cells Vs Heat Engines: Fuel cell efficiency is not limited by the Carnot cycle

The Carnot efficiency is a ratio of temperatures, while the fuel cell efficiency is a ratio of energy changes for a reaction.

What is the Carnot cycle?

The Carnot cycle is a theoretical ideal thermodynamic cycle. It provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work. A heat engine converts heat or thermal energy to mechanical energy,

What is a Fuel cell?

A fuel cell uses the chemical energy of hydrogen or another fuel to produce electricity.

Difference

The difference is Carnot cycle sets a theoretical upper limit for heat or thermal energy to convert to mechanical energy while a fuel cell uses chemical energy to convert to electrical energy. These fuel cells are seen as beneficial because their operation produces no carbon dioxide. Internal combustion engines produce carbon dioxide as a product of the combustion of fossil fuel with oxygen, and the release of this carbon dioxide into the atmosphere is thought to contribute to a “greenhouse effect”. Another advantage is the potentially higher efficiency of the hydrogen fuel cell compared to that of an internal combustion engine. This difference in efficiency will be discussed in this post

Carnot cycle and its efficiency

Essentially, the Carnot cycle consists of [1] Isothermal expansion. Heat is transferred reversibly from the high-temperature reservoir at constant temperature TH (isothermal heat addition or absorption - boiler) [2] Isentropic (reversible adiabatic) expansion of the gas (isentropic work output - turbine ) [3] Isothermal compression. Heat transferred reversibly to the low-temperature reservoir at constant temperature TC. (isothermal heat rejection - condenser) and [4] Adiabatic reversible compression - pump

Thermodynamics of Carnot cycle

Since the concept involves the cycle is theoretically reversible, there is no generation of entropy during the cycle; entropy is conserved. During the cycle, an arbitrary amount of entropy ΔS is extracted from the hot reservoir and deposited in the cold reservoir. Since there is no volume change in either reservoir, they do no work, and during the cycle, an amount of energy Th x ΔS is extracted from the hot reservoir and a smaller amount of energy Tc x ΔS is deposited in the cold reservoir. The difference between the two energies (Th-Tc) ΔS is equal to the work done by the engine.

The thermal efficiency of such a cycle is the ratio of the work recovered from the cycle to the heat energy input to the cycle.. Mathematically, this is expressed as

Qin = Wout + Qout

In this case, Qin is the heat energy input from the fuel combusted in the engine, W out is the mechanical work output from the engine, and Qout is waste heat that is carried out of the engine in the combustion product gases.

The efficiency, η ideal is thus, η ideal = W out / Q in = [Q in - Q out] / Q in. At constant volume heat capacity for air in the engine, the efficiency can also be stated as,

η ideal = ([T2-T1] - [T4-T3]) / [T2-T1] or, 1- [T4-T3]/[T2-T1] or, 1- [Cold heat reservoir/Hot reservoir temperature].

Carnot efficiency

The Carnot Efficiency is, therefore, the theoretical maximum efficiency one can get when the heat engine is operating between two temperatures: The temperature at which the high-temperature reservoir operates (T hot). The temperature at which the low-temperature reservoir operates (T cold). The efficiency of a Carnot engine depends solely on the temperatures of the hot and cold reservoirs. In other words, Carnot's theorem states that all heat engines are a function of the T cold / T hot ratio. The smaller this ratio, the larger is the efficiency of a heat engine. The ground reality is for the range of compression ratios (the ratio of minimum and maximum volumes in the engine cylinder as it reciprocates) typical of a gasoline engine, this maximum efficiency is only about 40 to 60 percent. And because this is the ideal efficiency, the actual efficiency will be even lower.

Fuel cell

A fuel cell is a device that generates electricity through an electrochemical reaction, not by combustion. The fuel cell does not generate energy, but just transforms the energy contained in the hydrogen and oxygen fuel into useful electrical energy output. In a fuel cell, hydrogen and oxygen are combined to generate electricity, heat, and water. A fuel cell is composed of an anode, cathode, and an electrolyte membrane. A typical fuel cell works by passing hydrogen through the anode of a fuel cell and oxygen through the cathode. At the anode site, a catalyst splits the hydrogen molecules into electrons and protons, H2 -- > H+ + H+ + 2e. The protons pass through the porous electrolyte membrane, while electrons can’t. The electrons are forced through an outer circuit, generating an electric current and excess heat. At the cathode, another catalyst causes ions, electrons, and oxygen to react, to produce water molecules, H+ + H+ + 2e + O2 -- > H2O + Heat. 

H2 -- > H+ + H+ + 2e [At anode]

Electrons in circulation between anode and cathode -- > Electricity

H+ + H+ + 2e + O2 -- > H2O + Heat [Cathode]

At cathode --- > Heat

Thermodynamics of Fuel cell

Thermodynamics controlled chemical reaction 2H2 (g) + O2 (g) → 2H2O (g) + Energy

A negative Gibbs free energy change ΔG = - 228.6 kJ /mol drives the oxidation of H2 by spontaneously supplying energy with no recharge requirement.

Thermodynamic data

The energy content of the fuel is the enthalpy change for the reaction, which in this case is, ΔH = - 241.8 kJ /mol For the overall reaction, at room temperature, the free energy change of the reaction, producing water vapor, is ΔG = -228.6 kJ/mol. The efficiency is the ratio of the maximum available work from the reaction’s free energy to the enthalpy change of the reaction, or

η ideal = ΔG / ΔH x 100 = 94.5

ΔH is total stored energy available for the reaction and ΔG is the free energy available that generates electrical work.

For the reaction of the fuel cell, the ideal efficiency is approximately 94%. This much higher theoretical efficiency makes fuel cells attractive

The fuel cell efficiency is not limited by the Carnot cycle.

Since fuel cells and batteries can generate useful power when all components of the system are at the same temperature T=T {H}=T {C} they are clearly not limited by Carnot's theorem, which states that no power can be generated when T {H}=T {C} The fuel cell and heat engine efficiencies are both constrained by the second law of thermodynamics and neither one is able to break this law.

The intrinsic difference between fuel cells (electrochemical systems) and heat engines (combustion engines) efficiencies is a fundamental one with regard to the conversion of chemical energy of reactions into electrical work. The single reason has been shown to be due to the combustion irreversibility of the latter and this has led to the statement that fuel cell efficiency is not limited by the Carnot cycle.

Does Fuel cell follow the 2nd law of thermodynamics?

Any system producing energy obeys the laws of thermodynamics. The concepts enthalpy, specific heat, entropy and Gibbs free energy are related to the reacting systems in fuel cells. Gibbs free energy is the thermodynamic potential that measures the reversible work by a thermodynamic system at constant pressure and temperature.

Do fuel cells degrade? This is mainly caused by the starts/stops, acceleration/deceleration, membrane humidity variation, and a high load of the engine. When the vehicle operates on various driving patterns, the fuel cell will degrade which eventually affects the fuel economy.

Carnot cycle vs Fuel cell: Is it a fair comparison? Different dimensions

Carnot cycle deals with the conversion of thermal energy to mechanical energy while Fuel cells convert chemical energy to electricity. However, both work within the domain of thermodynamics and inside the boundary of the 2nd law of thermodynamics.

The Carnot efficiency has little practical value. It is a maximum theoretical efficiency of a hypothetical engine. Even if such an engine could be constructed, it would have to be operated at infinitesimally low velocities to allow the heat transfer to occur. It would be very efficient, but it would generate no power. The same applies to the theoretical fuel cell efficiency: The fuel cell operating at theoretical efficiency would generate no current and therefore it would be of no practical value.

The theoretical efficiency of high-temperature fuel cells may be lower than the theoretical (Carnot) efficiency of a heat engine operating between the same temperatures. Although this may be correct, it has no relevance to the fuel cell, where there is no flame and the theoretical efficiency is determined by the ratio between Gibbs free energy and enthalpy of the hydrogen/oxygen reaction

Credit: Google