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Thermodynamics operators

21 operators in the thermodynamics category of the live registry. Compose them in a contract or call POST /api/zeq/compute — KO42 is always on, plus up to three more per call.

How it computes: dedicated closed-form solver solveTD — real equations over CODATA-2018 constants; where an operator needs a series/matrix/field a scalar cannot express, it refuses honestly. See the solvers.

OperatorDescriptionEquation
FEP0Helmholtz free energy from the partition function: F = -k_BT ln Z.∫(∂log f/∂θ)² f dx
MAXRELMaxwell relations: the four thermodynamic identities from the equality of mixed second partials of the potentials, e.g. (∂S/∂V)_T = (∂P/∂T)_V.(∂S/∂V)_T = (∂P/∂T)_V
RTEO9Heat equation with volumetric source term governing temperature evolution by diffusion.\frac{\partial T}{\partial t} = \alpha\nabla^2 T + \frac{q}{\rho c_p}
TH1First law of thermodynamics: internal energy change equals heat added minus work done.\Delta U = Q - W
TH10Thermal pressure coefficient relating pressure change to temperature change at constant volume.\left(\frac{\partial P}{\partial T}\right)_V = \frac{\alpha}{\kappa_T}
TH11Enthalpy defined as internal energy plus pressure-volume product.H = U + PV
TH12Chemical potential: partial derivative of Gibbs free energy with respect to particle number.\mu = \left(\frac{\partial G}{\partial N}\right)_{T,P}
TH13Fundamental thermodynamic relation combining first and second laws with chemical work.dU = TdS - PdV + \mu dN
TH14Heat capacity at constant volume as the partial derivative of internal energy with respect to temperature.C_V = \left(\frac{\partial U}{\partial T}\right)_V
TH15Thermal conductivity defined through Fourier's law of heat conduction.\kappa = \frac{dQ/dt}{A \cdot dT/dx}
TH2Ideal gas law relating pressure, volume, amount, and temperature of an ideal gas.PV = nRT
TH3Second law of thermodynamics: entropy of an isolated system never decreases.\Delta S \geq \frac{Q}{T}
TH4Carnot efficiency: maximum possible efficiency of a heat engine between two temperatures.\eta = 1 - \frac{T_C}{T_H}
TH5Boltzmann entropy: S = k_B ln(Omega), connecting thermodynamic entropy to microstates.S = k_B \ln \Omega
TH6Helmholtz free energy: thermodynamic potential for systems at constant temperature and volume.F = U - TS
TH7Gibbs free energy: thermodynamic potential for systems at constant temperature and pressure.G = H - TS
TH8Mayer relation: difference between heat capacities at constant pressure and constant volume.C_p - C_v = nR
TH9Adiabatic process law: pressure times volume to the gamma power is constant.PV^\gamma = \text{const}
TTHIRDThird law of thermodynamics: the entropy of a perfect crystal approaches zero as the absolute temperature approaches zero, S → 0 as T → 0.S → 0 as T → 0
TZEROZeroth law of thermodynamics: if two systems are each in thermal equilibrium with a third, they are in equilibrium with each other — the transitivity that makes temperature well-defined.A~C ∧ B~C ⟹ A~B
VDW1Van der Waals equation of state for a real gas: (P + a·n²/V²)(V − n·b) = nRT — corrects the ideal-gas law for molecular attraction (a) and finite molecular volume (b).(P + a n²/V²)(V − nb) = nRT

Compute one — a real call​

Ask the operator which inputs it needs (the honesty contract refuses empty inputs rather than inventing them):

curl -sS -X POST https://zeqsdk.com/api/zeq/operator-spec \
  -H "Content-Type: application/json" \
  -d '{"operator":"FEP0"}'

See also​