The efficiency improvement of high-temperature electrolysis is best appreciated by assuming the electricity used comes from a heat engine, and then considering the amount of heat energy necessary to produce one kg hydrogen (141.86 megajoules), both in the HTE process itself and also in producing the electricity used. At 100°C, 350 megajoules of thermal energy are required (41% efficient). At 850°C, 225 megajoules are required (64% efficient).
A brief explanation on calculating the efficiency of an HTE electrolytic cell is available on the website of Solid Cell Inc at: http://www.solidcell.net/electrolyzer
HTE does not provide a means to bypass the inherent inefficiency of a heat engine, by producing hydrogen which is then converted back to electricity in a fuel cell. (Any such efficiency improvement would allow the theoretical construction of a perpetual motion machine, which would violate the Second Law of Thermodynamics, which is impossible.) Thus any economic advantage to be gained from using HTE must come from supplying chemical processes which use hydrogen as a feedstock and not as a power source (such as the petrochemical or fertilizer industries), or motive processes for which hydrogen is a better energy carrier than electricity (rockets are an example, cars are not yet an example).
High-temperature electrolysis cannot compete with the chemical conversion of hydrocarbon or coal energy into hydrogen, as none of those conversions are limited by heat engine efficiency. Thus the possible supplies of cheap high-temperature heat for HTE are all nonchemical, including nuclear reactors, concentrating solar thermal collectors, and geothermal sources. HTE has been demonstrated in a laboratory at 108 kilojoules (thermal) per gram of hydrogen produced, but not at a commercial scale,The first commercial generation IV reactors are expected around 2030.
Given a cheap, high-temperature heat source, other hydrogen production methods are possible. In particular, see the thermochemical sulfur-iodine cycle. Thermochemical production might reach higher efficiencies than HTE because no heat engine is required. However, large-scale thermochemical production will require significant advances in materials that can withstand high-temperature, high-pressure, highly-corrosive environments.
The market for hydrogen is large (50 million metric tons/year in 2004, worth about $135 billion/year) and growing at about 10% per year (see hydrogen economy). The two major consumers are currently oil refineries and fertilizer plants (each consume about half of all production). Should hydrogen-powered cars become widespread, their consumption would greatly increase the demand for hydrogen.
During electrolysis, the amount of electrical energy that must be added equals the change in Gibbs free energy of the reaction plus the losses in the system. The losses can (theoretically) be arbitrarily close to zero, so the maximum thermodynamic efficiency of any electrochemical process equals 100%. In practice, the efficiency is given by electrical work achieved divided by the Gibbs free energy change of the reaction.
In most cases, such as room temperature water electrolysis, the electric input is larger than the enthalpy change of the reaction, so some energy is released as waste heat. In some other cases however, for instance in the electrolysis of steam into hydrogen and oxygen at high temperature, the opposite is true. Heat is absorbed from the surroundings, and the heating value of the produced hydrogen is higher than the electric input. In this case the efficiency relative to electric energy input can be said to be greater than 100%. The maximum theoretical efficiency of a fuel cell is the inverse of that of electrolysis. It is thus impossible to create a perpetual motion machine by combining the two processes.