Ericsson Cycle.

The Ericsson cycle takes its working fluid through 4 processes and returns it to the state it began in. In order, those are:

1. Isothermal expansion
2. Constant-pressure cooling through the regenerator
3. Isothermal compression
4. Constant-pressure heating from the regenerator

You will find it in intercooled, reheated and regenerated gas turbines approximate it. At the standard set-up above — pressure ratio 8, hot reservoir 900 K, cold reservoir 300 K, regenerator effectiveness 1 — it reaches a thermal efficiency of 66.67%, against a Carnot limit of 66.67% for the same temperature span. The net work is 358.1 kJ/kg, from 537.1 kJ/kg of heat in and 179 kJ/kg rejected.

Its efficiency has a closed form: η → 1 − T_C/T_H as ε → 1. The simulator above does not use it — it solves the state points and divides net work by heat in — but the two agree to machine precision, and the test suite behind this page checks that on every build.

Switch the diagram pane between P–v and T–s and watch the same cycle change costume. On the pressure–volume plot the area inside the loop is the net work per kilogram of working fluid, because work is the integral of P dv. On the temperature–entropy plot the area inside the loop is the net heat, because heat in a reversible process is the integral of T ds.

Those two areas are the same number. That is the first law applied to a closed loop: the fluid ends where it started, so its internal energy has not changed, so everything that went in as heat came out as work. Two different pictures, one arithmetic.

The T–s view is the more revealing of the two once you are comfortable with it, because it shows the temperature at which heat crossed the boundary — and that, not the amount, is what decides how much of it can become work.

John Ericsson was a Swedish-American engineer best remembered for the ironclad USS Monitor, but he spent decades on hot-air engines and on solar power. The cycle named after him replaces the Stirling cycle’s two constant-volume legs with two constant-pressure ones, and keeps the regenerator.

The change matters because constant pressure is what steady flow does naturally. A Stirling engine needs a sealed cylinder whose volume is held while heat moves; an Ericsson cycle can be built as a continuous flow of gas through heat exchangers, which is how turbomachinery works.

Give it a perfect regenerator and this cycle reaches the Carnot efficiency, exactly as Stirling does. Set both to the same two temperatures on this page and the efficiency cards will agree to the last digit. The legs between the isothermals do not matter to the answer, provided the heat they exchange is recovered rather than thrown away.

That is worth sitting with. Two cycles with different shapes, different diagrams and different machinery arrive at precisely the same number, because what sets the answer is the temperature at which heat crosses the boundary — and with ideal regeneration, all of it crosses at just two temperatures.

Nobody builds a true Ericsson engine. Isothermal compression and expansion require heat exchange at exactly the rate work is being done, continuously, along the whole process — which no real compressor or turbine does.

What industry builds is the approximation: a gas turbine with intercooling between compressor stages, reheat between turbine stages, and a recuperator recovering exhaust heat into the compressor discharge. Enough intercooling stages approach isothermal compression; enough reheat stages approach isothermal expansion; the recuperator is the regenerator. The Ericsson cycle is the limit that arrangement is heading towards.

Each of those three additions costs a large heat exchanger, and heat exchangers are heavy, expensive and full of pressure drop. That is why the arrangement turns up in stationary power plant, where mass does not matter and fuel does, and almost never in aircraft, where the reverse is true. The cycle you can build is always the one whose hardware you can afford to carry.