### Solar Ceria

July 7, 2011

One fundamental principle of thermodynamics is that you need a temperature difference to do work. This was discovered in 1824 by Sadi Carnot in his investigation of heat engines, and this principle is codified in the second law of thermodynamics. Carnot defined a maximum efficiency, η, as
η = 1 - (TC/TH)

where TC is the temperature of a cold reservoir, and TH is the temperature of a hot reservoir. When there is no temperature differential, TH is equal to TC, and the efficiency is zero.

This idea that a temperature differential provides work is nicely illustrated in the drinking bird toy that I showed in a previous article (Second Law of Thermodynamics, February 7, 2011). That article also discussed the second law and the impossibility of perpetual motion machines. The differential temperature in the drinking bird is provided by evaporative cooling that provides a slightly cooler temperature below ambient. There's a temperature differential, so work (the dipping action) can be done. Hot engines work best, which is somewhat of a battle cry for turbine engine designers.

When we want to harvest solar energy, photovoltaics are a good choice for small to medium-sized installations. The largest economical photovoltaic array would be one that powers a large building. Googleplex is a good example, since it has a solar installation that generates 1.6 megawatts, which is about 30% of the power demand for this corporate center.[1]

Solar thermal is the next step in power generation. In a recent article (Solar Nevada, June 6, 2011), I discussed the Crescent Dunes Solar Energy Project being constructed near Las Vegas that is rated at 110-megawatts. This installation uses mirrors to focus light onto a reactor that heats molten salt. The heat from the molten salt is used to create steam to drive a turbine generator. There's another solar thermal method that's being developed by materials scientists at the California Institute of Technology (Pasadena, CA) that makes use of the thermodynamics of the equilibrium between cerium oxide and its formative elements.[2-3]

Cerium oxide, a stable oxide that's also called ceria, is formed from the elements in a highly exothermic reaction:
Ce + O2 -> CeO2

Stable, of course, is a relative term, since, at a given temperature, there is always a small fraction of unreacted cerium available and an associated partial pressure of oxygen. At room temperature, the equilibrium pressure of oxygen over ceria is laughably small. It's just 2.3 x 10-180 atmospheres, so the idea that ceria is a very stable oxide is well founded.

When the temperature is increased, ceria starts to decompose, although just very slightly. The graph below shows the partial pressure of oxygen above ceria as a function of temperature, as calculated from its free energy of formation.[4]

Partial pressure of oxygen above ceria as a function of temperature, as calculated from the Gibbs Free Energy of formation.

Free energy data from Ref. 4.

Graph rendered by Gnumeric)

The idea that ceria will become oxygen deficient at high temperatures and will equilibrate by absorption of oxygen at low temperatures can be utilized to reduce water and carbon dioxide to form such useful products as hydrogen and carbon monoxide.

Hydrogen and carbon monoxide are precursors for the creation of syngas, which, in turn, is a precursor for liquid hydrocarbons. Catalysts will also convert hydrogen and carbon monoxide to methane. Using solar energy as the heat source makes this a solar energy process. A schematic of this process is shown in the figure, below.

Solar ceria thermal cycle.

The hot-side temperature is about 1650°C. Although the CalTech team obtained only a 0.7 to 0.8% efficiency in their process, they've estimated a 16-19% efficiency when things are optimized.[2] Even this higher percentage is a middling range for solar energy conversion, but the process might be an easy method of carbon sequestration.

If the carbon dioxide produced at a fossil fuel plant is processed to produce more carbon-containing fuel that's used at the plant, it would be a closed-cycle solar system.[3] The hydrogen production rate of 8.5–11.8 ml/gram-ceria is about the same as that of other solid-state thermochemical cycles, but one problem is the need for an extremely inert atmosphere at the oxygen release stage.[2]

### References:

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