An external combustion engine that converts heat to work by cyclically heating and cooling a gas between two spaces. Invented by Robert Stirling in 1816.
Why does it equal Carnot efficiency?
An ideal Stirling cycle with perfect regeneration consists of reversible processes only. By Carnot's theorem, all reversible cycles operating between the same temperatures achieve Carnot efficiency.
What are practical applications?
Radioisotope thermoelectric generators for spacecraft, silent submarine propulsion, and solar thermal power. Power density is lower than gas engines.
What does the regenerator do?
A heat exchanger that stores heat from isochoric cooling and returns it during isochoric heating, allowing the cycle to achieve Carnot efficiency.
π
I can see the simulation updating, but what exactly is being calculated here?
π
Great question! The simulator solves the governing equations in real time as you move the sliders. Each parameter you control directly affects the physical outcome you see in the graph. The key is to build an intuitive feel for how each variable influences the result β that's how engineers develop physical judgment.
π
So when I increase this parameter, the curve shifts significantly. Is that a linear relationship?
π
It depends on the model. Some relationships are linear, but many engineering phenomena are nonlinear. Try moving the sliders to extreme values and see if the output changes proportionally β if the graph shape changes, that's a sign of nonlinearity. This hands-on exploration is exactly what simulations are best for.
π
Where is this kind of analysis actually used in practice?
π
Constantly! Engineers run these calculations during the design phase to quickly screen parameters before investing in expensive physical tests or detailed finite element simulations. Getting comfortable with these simplified models is a real engineering skill.
Set hot reservoir temperature (TH_val in Kelvin, typical range 600β800 K for air engines) and cold reservoir temperature (TC_val, typically 300β400 K ambient)
Define swept volume V1_val in liters (range 0.5β5 L for small demonstration engines)
Click animate to visualize the four-stroke cycle on the P-V diagram: isothermal expansion at TH, isochoric cooling to TC, isothermal compression at TC, and isochoric heating back to TH
Compare displayed thermal efficiency (Ξ·_Stirling) against theoretical Carnot efficiency (Ξ·_Carnot = 1 β TC/TH) to assess real-cycle losses
Worked Example
Configure a beta-type Stirling engine: TH = 700 K, TC = 300 K, V1 = 2.0 L. The simulator computes Carnot limit as Ξ·_Carnot = 1 β 300/700 = 0.571 or 57.1%. The actual Stirling cycle with ideal gas assumptions yields approximately Ξ·_Stirling β 0.48 or 48%, reflecting regenerator losses and finite temperature differences. The P-V loop area represents net work output per cycle; increasing volume ratio (V_max/V_min) expands the loop and work production.
Practical Notes
Real hardware (e.g., Ericsson or Gifford-McMahon coolers) achieves 35β45% efficiency due to imperfect heat exchange and mechanical friction; this simulator assumes reversible processes
Larger ΞT = TH β TC (e.g., 500 K difference) increases both Carnot and Stirling efficiency; typical cryogenic systems operate at TH = 300 K, TC = 20 K for 93% Carnot potential
Observe how expansion volume ratio affects cycle power: doubling V1 while holding TH and TC constant increases absolute work but does not improve efficiency