Visualize the ideal Ericsson cycle, built from two isothermal processes and two constant-pressure processes. Adjust the hot and cold reservoir temperatures, the pressure ratio and the specific heat ratio to see the thermal efficiency, heat input, heat rejected, net work and regenerator heat update in real time, and confirm with a P-V diagram and charts how ideal regeneration delivers Carnot efficiency.
Parameters
Hot reservoir temperature T_hot
K
Temperature of the isothermal expansion (heat in)
Cold reservoir temperature T_cold
K
Temperature of the isothermal compression (heat out)
Pressure ratio r_p
Pressure ratio of the isothermal processes. Sets the size of heat and work
Specific heat ratio γ
c_p/c_v of air, about 1.40 at room temperature. Affects the regenerator heat
Results
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Thermal efficiency η (%)
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Carnot efficiency (compare) (%)
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Heat input q_in (kJ/kg)
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Heat rejected q_out (kJ/kg)
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Net work w_net (kJ/kg)
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Regenerator heat (internal) (kJ/kg)
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P-V diagram — cycle animation
1→2 isothermal compression (cold T_cold), 2→3 constant-pressure heating, 3→4 isothermal expansion (hot T_hot), 4→1 constant-pressure rejection. The enclosed area is the net work. The two constant-pressure processes cancel inside the ideal regenerator.
Thermal efficiency vs temperature ratio (equals Carnot)
Thermal efficiency of the Ericsson cycle with ideal regeneration. The two constant-pressure processes cancel internally, so heat crosses the boundary only at two temperatures, and the efficiency equals the Carnot value. T is the reservoir temperature.
Heat input q_in from the isothermal expansion at the hot temperature and net work w_net. R is the gas constant and r_p the pressure ratio. In an isothermal process the internal energy is unchanged, so the heat added becomes work.
$$q_{regen}=c_p\,(T_{hot}-T_{cold})$$
Heat exchanged in the two constant-pressure processes. An ideal regenerator passing this heat internally is what lets the cycle reach Carnot efficiency. c_p is the specific heat at constant pressure.
What is the Ericsson Cycle Simulator?
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I've never heard of the "Ericsson cycle". Is it different from the Otto and Diesel cycles?
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Yes, a completely different family. Otto and Diesel are internal-combustion cycles — they burn fuel inside the cylinder. The Ericsson cycle is more of an external-combustion idea: it assumes heat comes from outside. It has four processes: an isothermal compression at the cold side, a constant-pressure heating, an isothermal expansion at the hot side, and a constant-pressure rejection. So it is built from two isothermals and two constant-pressure processes. It was devised by the Swedish-American engineer John Ericsson in the 19th century.
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Isothermal means expanding the gas while keeping the temperature constant, right? Isn't that hard to do?
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As an ideal, yes. When a gas expands it normally cools, but here you keep adding just enough heat to hold the temperature steady. In an isothermal process of an ideal gas the internal energy stays constant, so all the heat you add turns into work. On the P-V diagram on the left, the 3→4 curve on the hot side and the 1→2 curve on the cold side — those two smooth hyperbolas — are the isothermal processes. The upper one is the hot T_hot, the lower one is the cold T_cold.
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The "Carnot efficiency" card and the "thermal efficiency" card are both exactly 70.0% by default. Is that a coincidence?
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No coincidence — that is the whole point of the Ericsson cycle. The Carnot efficiency is the upper limit the Second Law allows between a given pair of hot and cold reservoirs. Ordinary cycles never reach it. But the Ericsson cycle, with a trick called ideal regeneration, hits the Carnot efficiency exactly. That is why the two cards match. The Stirling cycle has the same property, and the two are known together as the "ideal regenerative cycles".
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What is this "ideal regeneration"? The "regenerator heat" card shows a big number.
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Good question. Regeneration means storing heat you would otherwise throw away and reusing it. During the constant-pressure rejection (4→1) the gas cools from hot to cold. The heat it gives off on the way is parked in a thermal store called a regenerator. During the constant-pressure heating (2→3) of the next cycle, that stored heat is handed back to the gas. The two constant-pressure processes then exchange no heat with the outside — they are completed internally. The "regenerator heat" card shows how much heat is circulating internally like that. By default it is 703 kJ/kg, even larger than the heat exchanged with the outside.
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I see. The constant-pressure heat cancels internally, so only the isothermal heat in and out remains, and that gives Carnot efficiency. Then why don't we make every engine an Ericsson engine?
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The gap between ideal and reality. Perfectly isothermal expansion and compression are almost impossible in a real machine, and no regenerator is lossless. A regenerator always needs a finite temperature difference, and any gas flowing through it causes a pressure drop. So real engines fall well below Carnot efficiency. Even so, the Ericsson cycle is a vital benchmark — it tells you "this is as far as theory can go" — and its idea lives on in solar-thermal power and regenerative gas turbines.
Frequently Asked Questions
The Ericsson cycle is an ideal cycle made of four processes: an isothermal compression at the cold temperature, a constant-pressure heat addition, an isothermal expansion at the hot temperature, and a constant-pressure heat rejection. In other words, it consists of two isothermal processes and two constant-pressure processes. Devised by the Swedish-American engineer John Ericsson, it is one of the two famous ideal regenerative cycles, alongside the Stirling cycle, which uses two isothermal and two constant-volume processes. With an ideal regenerator, the heat exchanged in the two constant-pressure processes cancels internally, so heat crosses the system boundary only at the two reservoir temperatures, and the cycle reaches Carnot efficiency.
The key is ideal regeneration. The heat needed for the constant-pressure heating and the heat given up during the constant-pressure cooling span the same temperature range and are equal in magnitude. Place a thermal store called a regenerator, and the heat released during constant-pressure cooling can be stored and handed back during the next constant-pressure heating. The two constant-pressure processes then exchange no heat with the outside; they are completed internally. What remains is the isothermal expansion at the hot temperature (heat in) and the isothermal compression at the cold temperature (heat out). That is exactly the Carnot condition — heat crosses the boundary only at two fixed temperatures — so the efficiency equals the Carnot value η = 1 − T_cold/T_hot.
When an ideal gas expands or is compressed isothermally, its internal energy does not change, so the heat added becomes work directly. The heat absorbed during isothermal expansion at the hot temperature is q_in = R·T_hot·ln(r_p), and the heat rejected during isothermal compression at the cold temperature is q_out = R·T_cold·ln(r_p), where R is the gas constant and r_p the pressure ratio. The net work is their difference, w_net = q_in − q_out = R·(T_hot − T_cold)·ln(r_p). Raising the pressure ratio increases heat and work logarithmically, but the efficiency η depends only on T_cold/T_hot and not on the pressure ratio.
It cannot be realized ideally. For the Ericsson cycle to deliver its efficiency, you need perfectly isothermal expansion and compression and a lossless ideal regenerator. In practice, holding the temperature constant while the gas expands is difficult, and any regenerator involves a finite temperature difference and a pressure drop. Real engines therefore fall well short of Carnot efficiency. Even so, the Ericsson cycle remains an important benchmark that marks the upper limit of achievable efficiency, and it continues to inspire the design of external-combustion engines, solar-thermal engines and regenerative gas turbines.
Real-World Applications
Design philosophy of regenerative gas turbines: Real gas turbines run on the Brayton cycle, but adding a "regenerator" that preheats the compressor-outlet air with the turbine exhaust raises efficiency. That is exactly the Ericsson idea of regeneration. If you stage the compression with intercooling and stage the expansion with reheat, the Brayton cycle approaches isothermal compression and expansion, and combined with regeneration it asymptotically approaches the Ericsson cycle — the Carnot efficiency. The Ericsson cycle marks the ultimate target that a regenerative gas turbine is striving toward.
Heat engines with external heating — solar, geothermal and waste heat: Because the Ericsson cycle heats its working gas from outside, it is an external-combustion cycle and an ideal model not only for fuel combustion but for any engine that extracts power from a heat source at a fixed temperature — solar, geothermal or waste heat. When estimating the upper-limit efficiency of solar-thermal power, where concentrated sunlight forms the hot reservoir and ambient air the cold reservoir, the Ericsson (or Stirling) cycle is the reference. In this tool, raising T_hot and lowering T_cold increases η, which is exactly the strategy of a hotter source and colder sink.
Teaching heat engines by contrast with the Stirling cycle: The Ericsson cycle appears in textbooks paired with the Stirling cycle as the "ideal regenerative cycles". The difference lies in the two processes that bracket the regeneration: Ericsson uses constant pressure, Stirling uses constant volume. Both reach the same conclusion — Carnot efficiency with ideal regeneration — making them an excellent pair for learning the thermodynamic essence that "with regeneration, a cycle reaches Carnot efficiency even if the process shapes differ". Seeing the Carnot efficiency and the thermal efficiency always match in this tool makes that essence tangible.
A benchmark for estimating the efficiency ceiling of a cycle: When conceiving a new heat engine or heat-recovery system, the first thing to know is "how efficient can it theoretically be for the given temperature difference?". That ceiling is the Carnot efficiency, and the Ericsson cycle expresses it in the concrete form of four processes. By comparing a real machine's efficiency with the Ericsson (Carnot) value, you can judge whether the system still has room for improvement or is already near the physical limit. This tool lets you check that ceiling quickly while varying the temperature ratio.
Common Misconceptions and Pitfalls
A common misconception is that "an Ericsson engine will deliver Carnot efficiency in practice too". The η = 1 − T_cold/T_hot shown by this tool is a theoretical value that assumes perfectly isothermal expansion and compression and a lossless ideal regenerator. In a real machine you cannot hold the temperature strictly constant while the gas expands, and any regenerator necessarily involves a finite temperature difference and a pressure drop. Add friction and heat leakage, and the net efficiency falls well below the Carnot value. Remember that the tool's number is "the ceiling you can aim for at this temperature difference", not the efficiency you will actually obtain.
Next, the assumption that "raising the pressure ratio r_p improves efficiency". As you move the pressure ratio in this tool, the heat input q_in, the heat rejected q_out and the net work w_net all increase logarithmically, but the thermal efficiency η does not move at all. That is because the pressure ratio does not appear in η = 1 − T_cold/T_hot. The pressure ratio sets "how much heat and work the cycle handles per cycle" — the size of the output — while efficiency is set by the temperature ratio alone. Output and efficiency are different things: a basic principle of heat-engine design surfaces right here.
Finally, the misconception that "the regenerator heat is wasted heat leaving the cycle". The regenerator heat q_regen = c_p·(T_hot − T_cold) is indeed a large value (about twice the net work by default), but it is not heat dumped to the outside. It is heat that merely circulates internally — the regenerator stores the heat released by the constant-pressure rejection and returns all of it to the gas in the next constant-pressure heating. In fact it is precisely this internal circulation that confines the external heat exchange to two temperatures and brings the cycle to Carnot efficiency. A large regenerator heat is not waste; it signals a design requirement to provide ample thermal capacity and heat-transfer performance in the regenerator.
How to Use
Set the hot reservoir temperature (tHotNum) between 300–1200 K and cold reservoir temperature (tColdNum) between 280–400 K using the sliders.
Adjust the pressure ratio (pRatioNum) from 2 to 8 to define the cycle's pressure envelope across isothermal and isobaric processes.
Specify the working fluid's heat capacity ratio gamma (gammaValNum) typically 1.4 for air or 1.67 for helium.
Click simulate to generate the P-V diagram, calculate thermal efficiency η, and compare against Carnot efficiency for the given temperature limits.
Worked Example
Consider a helium Ericsson cycle: T_hot = 900 K, T_cold = 300 K, pressure ratio = 5, gamma = 1.67. The simulator computes two isothermal processes at 900 K and 300 K, connected by two constant-pressure expansions/compressions at P_low and P_high = 5·P_low. Heat input q_in ≈ 450 kJ/kg occurs during isothermal expansion at high temperature. Heat rejection q_out ≈ 150 kJ/kg during isothermal compression at low temperature. Net work w_net ≈ 300 kJ/kg. Thermal efficiency η = 300/450 ≈ 66.7%, versus Carnot limit η_Carnot = (900–300)/900 = 66.7%, confirming regenerator effectiveness. Internal regenerator heat recovery ≈ 285 kJ/kg.
Practical Notes
Higher pressure ratios increase net work output but reduce relative efficiency gain over Carnot due to irreversibilities in real constant-pressure processes.
The Ericsson cycle matches Carnot efficiency only when the regenerator (internal heat exchanger) operates perfectly; use this simulator to assess regenerator duty in kJ/kg.
For industrial gas turbine configurations, pressure ratios 4–6 and T_hot/T_cold ratios near 3 optimize specific work while maintaining manufacturing feasibility.
Helium working fluid (gamma = 1.67) yields higher specific work than air (gamma = 1.4) at identical temperature and pressure ratios due to superior thermal properties.