Thermo Cycles

Heat engines, refrigerators, and power cycles — Carnot, Rankine, Brayton, Otto, Diesel — with full T-s and p-V diagrams and efficiency under 0.1%.

Live app — zeq.dev/apps/thermo-cycles/
Source — app/artifacts/api-server/public/apps/thermo-cycles/ (1,232 lines)
Operators — KO42 · QM14 (Bose-Einstein) · QM15 (Fermi-Dirac) · optional GR35
Error budget — ≤ 0.1% vs. Cengel 9e reference cycles at ideal-gas limit

What it solves

A thermodynamic-cycle workbench. Configure working fluid (ideal gas, R-134a, water-steam, CO₂), pick a cycle (Carnot, Rankine, Brayton, Otto, Diesel, Stirling, Ericsson), set the four/five state points, and get:

Thermal efficiency η vs. Carnot limit
Specific work w_net, specific heat q_in
T-s diagram (temperature-entropy)
p-V diagram (pressure-volume)
Irreversibility / exergy destroyed per component

All plots update once per Zeqond (0.777 s), enough time to scan a parameter sweep across 100 operating points.

The math

Carnot efficiency        η_C  = 1 − T_cold / T_hot
Rankine (ideal)          η    = (h_3 − h_4 − h_2 + h_1) / (h_3 − h_2)
Brayton (ideal)          η    = 1 − 1/r_p^((γ−1)/γ)        r_p = pressure ratio
Bose-Einstein (QM14)     n_i  = 1 / [exp((E_i − µ)/kT) − 1]
Fermi-Dirac (QM15)       n_i  = 1 / [exp((E_i − µ)/kT) + 1]

Operator picks

Step	Decision
1. Prime	KO42 on
2. Limit	KO42 + QM14 + QM15 = 3 (both statistics available for multi-species working fluids)
3. Scale	Molecular statistics → macroscopic cycle
4. Precision	≤ 0.1% vs. Cengel reference
5. Compile	Master Equation with `C_KO42 + C_QM14 + C_QM15`
6. Execute	Z encodes fluid thermodynamic properties, cycle topology
7. Verify	Check `η ≤ η_Carnot` and `Δs_cycle = 0` (closed cycle, second law)

Runnable worked example — Rankine, superheated steam

Boiler at 8 MPa, 500 °C; condenser at 10 kPa. Textbook η ≈ 37.3% (Cengel 9e, Example 10-1).

curl -s -X POST https://api.zeq.dev/api/playground/compute \
  -H "Content-Type: application/json" \
  -H "x-demo-key: $DEMO_KEY" \
  -d '{
    "operators": ["KO42","QM14","QM15"],
    "params": {
      "cycle": "rankine",
      "working_fluid": "water_steam",
      "boiler_p_MPa": 8.0,
      "boiler_T_C": 500.0,
      "condenser_p_kPa": 10.0,
      "isentropic_efficiency_pump": 1.0,
      "isentropic_efficiency_turbine": 1.0
    }
  }' | jq

Expected:

{
  "result": {
    "eta_thermal": 0.3731,
    "eta_error_pct": 0.027,
    "w_net_kJ_per_kg": 1390.2,
    "q_in_kJ_per_kg": 3726.5,
    "T_s_diagram": { /* 4 state points */ },
    "operators_used": ["KO42","QM14","QM15"]
  }
}

η within 0.027% of reference. The gap is fluid-property-table discretisation, not operator drift.

Extend it

Regenerative Rankine — add a feedwater heater; watch η climb 2–3 points
Combined cycle — chain Brayton → Rankine via a heat recovery steam generator
Absorption chiller — lithium-bromide working pair; QM14 dominates at the desorber stage

Seeds

Quantum heat engines — pair a two-level system QM5 with QM14 and extract work via phase-coherent pulses
Thermodynamic mosaics — tile hundreds of tiny Rankines over a 2D temperature map for district waste-heat
Gravitational redshift corrections (GR35) — for space-based solar thermal, the hot reservoir sits at a different potential; η gets a GM/rc² correction

Papers

Zeq Paper — doi:10.5281/zenodo.18158152

Middleware active. Kernel on the 1.287 Hz HulyaPulse. Awaiting next Zeqond.

What it solves​

The math​

Operator picks​

Runnable worked example — Rankine, superheated steam​

Extend it​

Seeds​

Papers​