Fuel, heat and wheels

Take a walk through six miniature power plants. Five of them are variations on one idea, and one of them, the solar farm, is a different idea. Each plant is a chain of energy conversions, and every link in the chain loses some energy as heat.

Heat plants (coal, gas, nuclear) follow one chain:

• fuel (chemical or nuclear energy) → heat → steam → turbine (spinning) → generator → electricity.

The fuel is burned, or in the nuclear case split, to make heat. The heat boils water. High-pressure steam spins a turbine. The turbine spins the generator you met in the last lesson. After the turbine the steam is cooled back into water, which needs a river, the sea or a cooling tower, and that cooling takes away a large amount of heat.

A gas plant can be a combined-cycle plant: hot gas first spins a gas turbine, like a jet engine; its still-hot exhaust then boils water for a second, steam turbine. Using the heat twice gives the highest efficiency of the heat plants.

Efficiency is the electricity delivered divided by the energy that went in: efficiency = E_out / E_in. Typical values (they vary with plant age and design):

• Coal: about 33 to 40 percent. The newest, hottest designs reach the mid-40s.
• Gas, combined cycle: about 55 to 60 percent.
• Nuclear: about 33 percent. Its steam is cooler than in a modern coal plant, for safety and materials reasons.
• Hydro: about 85 to 90 percent. No heat is involved; falling water pushes a turbine directly.
• Wind (whole turbine, real): about 35 to 50 percent of the wind's power. The theory limit is 59.3 percent (World 2).
• Solar PV module: about 18 to 23 percent of the sunlight that lands on it (World 3).

Why is a heat plant's efficiency limited? A heat engine can only turn part of the heat into work. The rest must be dumped into a cooler place. The best possible fraction, the Carnot efficiency, is 1 − T_cold / T_hot with temperatures in kelvin. Example: steam at 540 °C (813 K) and cooling water at 30 °C (303 K) give 1 − 303/813 ≈ 63 percent at the very most. Real plants have friction, leaks and pressure drops on top of that, so a real coal plant lands near 40 percent. Particle Lab, in its Heat Engines world, explores Carnot in depth.

Hydro, wind and solar do not burn anything and so do not face the Carnot limit. They have their own limits, which the next worlds explore.

What does the world's electricity come from? It changes every year. In 2024, according to the energy think tank Ember, roughly: coal about one third, gas about one fifth, hydro about one seventh, nuclear about one tenth, wind and solar together about 15 percent, with the rest from bioenergy and other sources. Treat these as round numbers for one year; they shift as new plants are built. Each country's mix differs a great deal: some run mostly on hydro, some mostly on gas, some mostly on coal or nuclear.