{"openapi":"3.1.0","info":{"title":"Thermodynamics and Heat Transfer","version":"1.0.0","description":"Ideal gas processes, Carnot efficiency and COP, conduction, convection and radiation, heat exchangers, mixing, water vapor pressure and thermal expansion. One call, one computed answer, no accounts or API keys. Machine-payable over x402.","x-guidance":"Thermodynamics and Heat Transfer: Ideal gas processes, Carnot efficiency and COP, conduction, convection and radiation, heat exchangers, mixing, water vapor pressure and thermal expansion. Use /ideal-gas-process for gas work and heat, /carnot-efficiency for engine efficiency and COP, /conduction-heat-transfer for wall and pipe heat flow, /convection-radiation for Newton cooling and radiation, /heat-exchanger-lmtd for LMTD and effectiveness-NTU, /specific-heat-mixing for mixed temperatures and phase change, /saturation-pressure-water for vapor pressure and /thermal-expansion for length and volume change. Each paid GET returns a computed verdict with the reasons, the source and what was NOT checked. A verdict of UNVERIFIED means a lookup failed: treat it as unknown. No account or key: pay per call in USDC over x402."},"servers":[{"url":"https://thermo-heat-calc.x402tookit.com"}],"paths":{"/carnot-efficiency":{"get":{"operationId":"carnot_efficiency","summary":"Carnot limit for a heat engine, refrigerator and heat pump from hot and cold absolute temperatures, with work and heat flows.","description":"Carnot limit for a heat engine, refrigerator and heat pump from hot and cold absolute temperatures, with work and heat flows.","tags":["carnot","efficiency","cop","heat-engine"],"parameters":[{"name":"hotK","in":"query","required":true,"description":"Hot reservoir ABSOLUTE temperature in kelvin (K = C + 273.15)","schema":{"type":"number"}},{"name":"coldK","in":"query","required":true,"description":"Cold reservoir ABSOLUTE temperature in kelvin, below hotK","schema":{"type":"number"}},{"name":"heatInputKw","in":"query","required":false,"description":"Heat drawn from the hot reservoir in kW, for engine work output and rejected heat","schema":{"type":"number"}},{"name":"coolingLoadKw","in":"query","required":false,"description":"Heat removed from the cold space in kW, for the refrigerator work input","schema":{"type":"number"}},{"name":"heatingLoadKw","in":"query","required":false,"description":"Heat delivered to the hot space in kW, for the heat-pump work input","schema":{"type":"number"}},{"name":"actualEfficiency","in":"query","required":false,"description":"Your real engine efficiency 0 to 1, to get the fraction of Carnot reached","schema":{"type":"number"}}],"responses":{"200":{"description":"The answer.","content":{"application/json":{"schema":{"type":"object","properties":{"verdict":{"type":["null","string"]},"summary":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"hotK":{"type":["null","number"]},"coldK":{"type":["null","number"]},"carnotEfficiency":{"type":["null","number"]},"carnotEfficiencyPct":{"type":["null","number"]},"copRefrigerator":{"type":["null","number"]},"copHeatPump":{"type":["null","number"]},"temperatureDifferenceK":{"type":["null","number"]},"engineWorkOutputKw":{"type":["null","number"]},"engineHeatRejectedKw":{"type":["null","number"]},"degraded":{"type":["boolean","null"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"source":{"type":["null","string"]},"asOf":{"type":["null","string"]},"disclaimer":{"type":["null","string"]}}},"example":{"verdict":"COMPUTED","summary":"Between 500 K and 300 K the Carnot engine efficiency is 40%, refrigerator COP 1.5, heat-pump COP 2.5.","reasons":["Temperatures must be absolute (kelvin); using Celsius gives wrong answers.","COP of the heat pump equals COP of the refrigerator plus 1 for the same reservoirs.","…1 more"],"hotK":500,"coldK":300,"carnotEfficiency":0.4,"carnotEfficiencyPct":40,"copRefrigerator":1.5,"copHeatPump":2.5,"temperatureDifferenceK":200,"engineWorkOutputKw":40,"engineHeatRejectedKw":60,"degraded":false,"notChecked":["irreversibilities, finite-rate heat transfer or real cycle limits (Carnot is an upper bound, not a prediction)","part-load and parasitic losses (fans, pumps, defrost)","…1 more"],"source":"computed locally (Carnot: eta = 1 - Tc/Th; COP refrigerator = Tc/(Th - Tc); COP heat pump = Th/(Th - Tc))","asOf":"2026-10-21T06:33:56.098Z","disclaimer":"Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting."}}}},"400":{"description":"A parameter was missing or out of range."},"402":{"description":"Payment Required"},"502":{"description":"The upstream source failed or timed out."}},"x-payment-info":{"price":{"mode":"fixed","currency":"USD","amount":"0.0200"},"protocols":[{"x402":{"network":"eip155:8453","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/carnot-efficiency"}},{"x402":{"network":"solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/carnot-efficiency"}},{"x402":{"network":"eip155:137","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/carnot-efficiency"}},{"x402":{"network":"eip155:42161","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/carnot-efficiency"}}]}}},"/conduction-heat-transfer":{"get":{"operationId":"conduction_heat_transfer","summary":"Steady conduction heat flow through a slab or cylinder wall of layers in series, with R-values and interface temperatures.","description":"Steady conduction heat flow through a slab or cylinder wall of layers in series, with R-values and interface temperatures.","tags":["conduction","heat-transfer","r-value","insulation"],"parameters":[{"name":"geometry","in":"query","required":true,"description":"slab (flat wall) or cylinder (pipe wall)","schema":{"type":"string"}},{"name":"layers","in":"query","required":true,"description":"Slab: thicknessM:conductivity pairs, hot side first, e.g. 0.2:0.72;0.05:0.04. Cylinder: outerRadiusM:conductivity pairs, inside out. Conductivity in W/(m K)","schema":{"type":"string"}},{"name":"hotC","in":"query","required":true,"description":"Hot-side temperature in degrees C (inside surface, or air if film coefficients are sent)","schema":{"type":"number"}},{"name":"coldC","in":"query","required":true,"description":"Cold-side temperature in degrees C, below hotC","schema":{"type":"number"}},{"name":"areaM2","in":"query","required":false,"description":"Slab area in m2 (default 1; slab only)","schema":{"type":"number"}},{"name":"innerRadiusM","in":"query","required":false,"description":"Cylinder inner radius in metres (cylinder only, required there)","schema":{"type":"number"}},{"name":"lengthM","in":"query","required":false,"description":"Cylinder length in metres (default 1; cylinder only)","schema":{"type":"number"}},{"name":"hInner","in":"query","required":false,"description":"Hot-side film coefficient in W/(m2 K); adds a convective resistance 1/(h A)","schema":{"type":"number"}},{"name":"hOuter","in":"query","required":false,"description":"Cold-side film coefficient in W/(m2 K); adds a convective resistance 1/(h A)","schema":{"type":"number"}}],"responses":{"200":{"description":"The answer.","content":{"application/json":{"schema":{"type":"object","properties":{"verdict":{"type":["null","string"]},"summary":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"geometry":{"type":["null","string"]},"totalResistanceKPerW":{"type":["null","number"]},"heatFlowW":{"type":["null","number"]},"temperatureDifferenceK":{"type":["null","number"]},"stack":{"type":["array","null"],"items":{"type":"object","properties":{"element":{"type":["null","string"]},"resistanceKPerW":{"type":["null","number"]},"hotSideC":{"type":["null","number"]},"coldSideC":{"type":["null","number"]}}}},"uOverallWPerM2K":{"type":["null","number"]},"rsiM2KPerW":{"type":["null","number"]},"rValueUs":{"type":["null","number"]},"heatFluxWPerM2":{"type":["null","number"]},"heatFlowPerMeterWPerM":{},"areaM2":{"type":["null","number"]},"degraded":{"type":["boolean","null"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"source":{"type":["null","string"]},"asOf":{"type":["null","string"]},"disclaimer":{"type":["null","string"]}}},"example":{"verdict":"COMPUTED","summary":"slab wall of 2 layers: heat flow 19.636 W for 30 K, total resistance 1.5278 K/W.","reasons":["Slab: R = thickness / (k A) per layer; resistances add in series; Q = deltaT / total R.","Temperatures step down across each element in proportion to its resistance (listed below).","…1 more"],"geometry":"slab","totalResistanceKPerW":1.5277778,"heatFlowW":19.636364,"temperatureDifferenceK":30,"stack":[{"element":"layer 1","resistanceKPerW":0.27777778,"hotSideC":20,"coldSideC":14.545455},{"element":"layer 2","resistanceKPerW":1.25,"hotSideC":14.545455,"coldSideC":-10}],"uOverallWPerM2K":0.65454545,"rsiM2KPerW":1.5277778,"rValueUs":8.675124,"heatFluxWPerM2":19.636364,"heatFlowPerMeterWPerM":null,"areaM2":1,"degraded":false,"notChecked":["contact resistance between layers","thermal bridges, edge effects and moisture in insulation","…2 more"],"source":"computed locally (Fourier: slab R = L/(kA); cylinder R = ln(r2/r1)/(2 pi k L); layers add in series; Q = deltaT / sum R)","asOf":"2026-10-21T06:33:56.360Z","disclaimer":"Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting."}}}},"400":{"description":"A parameter was missing or out of range."},"402":{"description":"Payment Required"},"502":{"description":"The upstream source failed or timed out."}},"x-payment-info":{"price":{"mode":"fixed","currency":"USD","amount":"0.0300"},"protocols":[{"x402":{"network":"eip155:8453","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/conduction-heat-transfer"}},{"x402":{"network":"solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/conduction-heat-transfer"}},{"x402":{"network":"eip155:137","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/conduction-heat-transfer"}},{"x402":{"network":"eip155:42161","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/conduction-heat-transfer"}}]}}},"/convection-radiation":{"get":{"operationId":"convection_radiation","summary":"Newton convection, Stefan-Boltzmann net radiation with emissivity, the radiation coefficient and combined heat loss.","description":"Newton convection, Stefan-Boltzmann net radiation with emissivity, the radiation coefficient and combined heat loss.","tags":["convection","radiation","stefan-boltzmann","heat-transfer"],"parameters":[{"name":"surfaceC","in":"query","required":true,"description":"Surface temperature in degrees C","schema":{"type":"number"}},{"name":"ambientC","in":"query","required":true,"description":"Surrounding fluid (air) temperature in degrees C","schema":{"type":"number"}},{"name":"areaM2","in":"query","required":true,"description":"Surface area in m2","schema":{"type":"number"}},{"name":"hConvection","in":"query","required":false,"description":"Convection coefficient h in W/(m2 K) (default 10, a typical still-air natural convection value)","schema":{"type":"number"}},{"name":"emissivity","in":"query","required":false,"description":"Surface emissivity 0 to 1 (default 0.9)","schema":{"type":"number"}},{"name":"surroundingsC","in":"query","required":false,"description":"Radiative surroundings temperature in degrees C (default: same as ambientC)","schema":{"type":"number"}}],"responses":{"200":{"description":"The answer.","content":{"application/json":{"schema":{"type":"object","properties":{"verdict":{"type":["null","string"]},"summary":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"surfaceK":{"type":["null","number"]},"ambientK":{"type":["null","number"]},"surroundingsK":{"type":["null","number"]},"convectionW":{"type":["null","number"]},"radiationW":{"type":["null","number"]},"totalW":{"type":["null","number"]},"radiationSharePct":{"type":["null","number"]},"hConvection":{"type":["null","number"]},"hRadiation":{"type":["null","number"]},"hCombined":{"type":["null","number"]},"fluxWPerM2":{"type":["null","number"]},"emissivity":{"type":["null","number"]},"stefanBoltzmann":{"type":["null","number"]},"degraded":{"type":["boolean","null"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"source":{"type":["null","string"]},"asOf":{"type":["null","string"]},"disclaimer":{"type":["null","string"]}}},"example":{"verdict":"HEAT_LOSS_FROM_SURFACE","summary":"Surface 100 C in 20 C air: convection 800 W + radiation 612.55 W = 1412.5 W (combined coefficient 17.66 W/(m2 K)).","reasons":["Convection (Newton): q = h A (Ts - Tinf).","Radiation: q = eps sigma A (Ts^4 - Tsur^4) with temperatures in kelvin.","…2 more"],"surfaceK":373.15,"ambientK":293.15,"surroundingsK":293.15,"convectionW":800,"radiationW":612.54741,"totalW":1412.5474,"radiationSharePct":43.3647,"hConvection":10,"hRadiation":7.6568426,"hCombined":17.656843,"fluxWPerM2":1412.5474,"emissivity":0.9,"stefanBoltzmann":5.670374419e-8,"degraded":false,"notChecked":["how to pick h (depends on geometry, flow and fluid; the default is only a still-air ballpark)","view factors and non-grey surfaces (the surface is treated as small and enclosed by the surroundings)","…1 more"],"source":"computed locally (Newton q = h A dT; net radiation q = eps sigma A (Ts^4 - Tsur^4), sigma = 5.670374419e-8 W/(m2 K4))","asOf":"2026-10-21T06:33:56.625Z","disclaimer":"Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting."}}}},"400":{"description":"A parameter was missing or out of range."},"402":{"description":"Payment Required"},"502":{"description":"The upstream source failed or timed out."}},"x-payment-info":{"price":{"mode":"fixed","currency":"USD","amount":"0.0200"},"protocols":[{"x402":{"network":"eip155:8453","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/convection-radiation"}},{"x402":{"network":"solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/convection-radiation"}},{"x402":{"network":"eip155:137","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/convection-radiation"}},{"x402":{"network":"eip155:42161","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/convection-radiation"}}]}}},"/heat-exchanger-lmtd":{"get":{"operationId":"heat_exchanger_lmtd","summary":"Heat exchanger LMTD (counterflow or parallel) with duty and area, or counterflow effectiveness-NTU outlet temperatures.","description":"Heat exchanger LMTD (counterflow or parallel) with duty and area, or counterflow effectiveness-NTU outlet temperatures.","tags":["heat-exchanger","lmtd","ntu","effectiveness"],"parameters":[{"name":"mode","in":"query","required":false,"description":"lmtd (default; needs all four temperatures) or ntu (counterflow; needs capacity rates and UA)","schema":{"type":"string"}},{"name":"hotInC","in":"query","required":true,"description":"Hot stream inlet temperature in degrees C","schema":{"type":"number"}},{"name":"coldInC","in":"query","required":true,"description":"Cold stream inlet temperature in degrees C","schema":{"type":"number"}},{"name":"hotOutC","in":"query","required":false,"description":"lmtd mode: hot stream outlet temperature in degrees C","schema":{"type":"number"}},{"name":"coldOutC","in":"query","required":false,"description":"lmtd mode: cold stream outlet temperature in degrees C","schema":{"type":"number"}},{"name":"arrangement","in":"query","required":false,"description":"lmtd mode: counterflow (default) or parallel","schema":{"type":"string"}},{"name":"uWPerM2K","in":"query","required":false,"description":"Overall heat transfer coefficient U in W/(m2 K), with areaM2 for duty, or alone with dutyW for the area","schema":{"type":"number"}},{"name":"areaM2","in":"query","required":false,"description":"Heat transfer area in m2 (lmtd mode, with uWPerM2K)","schema":{"type":"number"}},{"name":"dutyW","in":"query","required":false,"description":"Heat duty in watts (lmtd mode, with uWPerM2K, to find the required area)","schema":{"type":"number"}},{"name":"hotCapacityWPerK","in":"query","required":false,"description":"ntu mode: hot stream m cp in W/K","schema":{"type":"number"}},{"name":"coldCapacityWPerK","in":"query","required":false,"description":"ntu mode: cold stream m cp in W/K","schema":{"type":"number"}},{"name":"uaWPerK","in":"query","required":false,"description":"ntu mode: U x A in W/K","schema":{"type":"number"}}],"responses":{"200":{"description":"The answer.","content":{"application/json":{"schema":{"type":"object","properties":{"verdict":{"type":["null","string"]},"summary":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"mode":{"type":["null","string"]},"arrangement":{"type":["null","string"]},"deltaT1K":{"type":["null","number"]},"deltaT2K":{"type":["null","number"]},"lmtdK":{"type":["null","number"]},"arithmeticMeanDeltaTK":{"type":["null","number"]},"dutyW":{"type":["null","number"]},"requiredAreaM2":{},"uWPerM2K":{"type":["null","number"]},"hotRange":{"type":["null","number"]},"coldRange":{"type":["null","number"]},"correctionFactorParamR":{"type":["null","number"]},"correctionFactorParamP":{"type":["null","number"]},"degraded":{"type":["boolean","null"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"source":{"type":["null","string"]},"asOf":{"type":["null","string"]},"disclaimer":{"type":["null","string"]}}},"example":{"verdict":"COMPUTED","summary":"counterflow LMTD 44.8142 K (end differences 50 and 40 K); duty 44814.2 W.","reasons":["LMTD = (dT1 - dT2) / ln(dT1 / dT2) with dT1 = Th,in - Tc,out and dT2 = Th,out - Tc,in; equal end differences give LMTD = that difference.","Q = U A LMTD.","…1 more"],"mode":"lmtd","arrangement":"counterflow","deltaT1K":50,"deltaT2K":40,"lmtdK":44.814201,"arithmeticMeanDeltaTK":45,"dutyW":44814.201,"requiredAreaM2":null,"uWPerM2K":500,"hotRange":40,"coldRange":30,"correctionFactorParamR":1.33333,"correctionFactorParamP":0.375,"degraded":false,"notChecked":["multipass or crossflow correction factors (single-pass pure counterflow or parallel flow only)","fouling, property changes and phase change inside the exchanger","…1 more"],"source":"computed locally (LMTD = (dT1 - dT2)/ln(dT1/dT2); counterflow effectiveness e = (1 - exp(-NTU(1-Cr))) / (1 - Cr exp(-NTU(1-Cr))), e = NTU/(1+NTU) at Cr = 1)","asOf":"2026-10-21T06:33:56.875Z","disclaimer":"Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting."}}}},"400":{"description":"A parameter was missing or out of range."},"402":{"description":"Payment Required"},"502":{"description":"The upstream source failed or timed out."}},"x-payment-info":{"price":{"mode":"fixed","currency":"USD","amount":"0.0300"},"protocols":[{"x402":{"network":"eip155:8453","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/heat-exchanger-lmtd"}},{"x402":{"network":"solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/heat-exchanger-lmtd"}},{"x402":{"network":"eip155:137","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/heat-exchanger-lmtd"}},{"x402":{"network":"eip155:42161","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/heat-exchanger-lmtd"}}]}}},"/ideal-gas-process":{"get":{"operationId":"ideal_gas_process","summary":"Ideal gas isothermal, isobaric, isochoric or adiabatic process: final state, work, heat and internal energy change.","description":"Ideal gas isothermal, isobaric, isochoric or adiabatic process: final state, work, heat and internal energy change.","tags":["ideal-gas","thermodynamics","adiabatic","work-heat"],"parameters":[{"name":"process","in":"query","required":true,"description":"isothermal, isobaric, isochoric or adiabatic","schema":{"type":"string"}},{"name":"massKg","in":"query","required":true,"description":"Gas mass in kilograms","schema":{"type":"number"}},{"name":"initialPressureKpa","in":"query","required":true,"description":"Initial absolute pressure in kPa","schema":{"type":"number"}},{"name":"initialTemperatureK","in":"query","required":true,"description":"Initial absolute temperature in kelvin (K = C + 273.15)","schema":{"type":"number"}},{"name":"gas","in":"query","required":false,"description":"air (default), nitrogen, oxygen, helium, argon, hydrogen, carbon-dioxide or steam; or send gamma and gasConstantJPerKgK","schema":{"type":"string"}},{"name":"gamma","in":"query","required":false,"description":"Ratio of specific heats cp/cv, above 1 (custom gas; send with gasConstantJPerKgK)","schema":{"type":"number"}},{"name":"gasConstantJPerKgK","in":"query","required":false,"description":"Specific gas constant R in J/(kg K) (custom gas)","schema":{"type":"number"}},{"name":"finalPressureKpa","in":"query","required":false,"description":"Final pressure in kPa (send exactly one final-state value)","schema":{"type":"number"}},{"name":"finalVolumeM3","in":"query","required":false,"description":"Final volume in m3 (send exactly one final-state value)","schema":{"type":"number"}},{"name":"finalTemperatureK","in":"query","required":false,"description":"Final temperature in kelvin (send exactly one final-state value)","schema":{"type":"number"}}],"responses":{"200":{"description":"The answer.","content":{"application/json":{"schema":{"type":"object","properties":{"verdict":{"type":["null","string"]},"summary":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"process":{"type":["null","string"]},"gas":{"type":["null","string"]},"gamma":{"type":["null","number"]},"gasConstantJPerKgK":{"type":["null","number"]},"cvJPerKgK":{"type":["null","number"]},"cpJPerKgK":{"type":["null","number"]},"massKg":{"type":["null","number"]},"initialPressureKpa":{"type":["null","number"]},"initialTemperatureK":{"type":["null","number"]},"initialVolumeM3":{"type":["null","number"]},"finalPressureKpa":{"type":["null","number"]},"finalTemperatureK":{"type":["null","number"]},"finalVolumeM3":{"type":["null","number"]},"workByGasJ":{"type":["null","number"]},"heatAddedJ":{"type":["null","number"]},"internalEnergyChangeJ":{"type":["null","number"]},"enthalpyChangeJ":{"type":["null","number"]},"degraded":{"type":["boolean","null"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"source":{"type":["null","string"]},"asOf":{"type":["null","string"]},"disclaimer":{"type":["null","string"]}}},"example":{"verdict":"COMPUTED","summary":"adiabatic air process: T 300 to 365.7 K, p 100 to 200 kPa; work by gas -47.151 kJ, heat in 7.276e-15 kJ.","reasons":["Work W is done BY the gas (positive on expansion); Q is heat ADDED to the gas; first law Q = deltaU + W.","cv = R / (gamma - 1) = 717.63 and cp = gamma R / (gamma - 1) = 1004.7 J/(kg K); deltaU = m cv deltaT.","…1 more"],"process":"adiabatic","gas":"air","gamma":1.4,"gasConstantJPerKgK":287.05,"cvJPerKgK":717.625,"cpJPerKgK":1004.675,"massKg":1,"initialPressureKpa":100,"initialTemperatureK":300,"initialVolumeM3":0.86115,"finalPressureKpa":200,"finalTemperatureK":365.7041,"finalVolumeM3":0.5248768,"workByGasJ":-47150.902,"heatAddedJ":7.2759576e-12,"internalEnergyChangeJ":47150.902,"enthalpyChangeJ":66011.263,"degraded":false,"notChecked":["real-gas behaviour near condensation or high pressure","temperature-dependent specific heats (gamma is held constant)","…2 more"],"source":"computed locally (ideal gas pV = mRT; first law Q = dU + W; adiabatic T V^(gamma-1) and p V^gamma constant)","asOf":"2026-10-21T06:33:57.138Z","disclaimer":"Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting."}}}},"400":{"description":"A parameter was missing or out of range."},"402":{"description":"Payment Required"},"502":{"description":"The upstream source failed or timed out."}},"x-payment-info":{"price":{"mode":"fixed","currency":"USD","amount":"0.0300"},"protocols":[{"x402":{"network":"eip155:8453","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/ideal-gas-process"}},{"x402":{"network":"solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/ideal-gas-process"}},{"x402":{"network":"eip155:137","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/ideal-gas-process"}},{"x402":{"network":"eip155:42161","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/ideal-gas-process"}}]}}},"/saturation-pressure-water":{"get":{"operationId":"saturation_pressure_water","summary":"Saturation vapor pressure of water from 1 to 100 C by Antoine and Magnus equations, or the boiling point at a pressure.","description":"Saturation vapor pressure of water from 1 to 100 C by Antoine and Magnus equations, or the boiling point at a pressure.","tags":["vapor-pressure","antoine","magnus","boiling-point"],"parameters":[{"name":"temperatureC","in":"query","required":false,"description":"Water temperature in degrees C, 1 to 100 (send this or pressureKpa)","schema":{"type":"number"}},{"name":"pressureKpa","in":"query","required":false,"description":"Absolute pressure in kPa, 0.65 to 101.4, to get the boiling temperature (Antoine inverse)","schema":{"type":"number"}}],"responses":{"200":{"description":"The answer.","content":{"application/json":{"schema":{"type":"object","properties":{"verdict":{"type":["null","string"]},"summary":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"temperatureC":{"type":["null","number"]},"temperatureK":{"type":["null","number"]},"antoineKpa":{"type":["null","number"]},"antoineMmHg":{"type":["null","number"]},"antoineBar":{"type":["null","number"]},"magnusKpa":{"type":["null","number"]},"magnusMinusAntoinePct":{"type":["null","number"]},"boilingPointAtAtmosphereC":{},"degraded":{"type":["boolean","null"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"source":{"type":["null","string"]},"asOf":{"type":["null","string"]},"disclaimer":{"type":["null","string"]}}},"example":{"verdict":"COMPUTED","summary":"Water at 25 C: saturation pressure 3.15793 kPa (Antoine) or 3.16174 kPa (Magnus).","reasons":["Antoine (Stull/NIST constants A 8.07131, B 1730.63, C 233.426, pressure in mmHg, T in C) fits 1 to 100 C to within about 1% of steam tables (about 0.5% above 20 C).","Magnus (Alduchov and Eskridge) is accurate to about 0.4% from -40 to 60 C and drifts to about 2.7% high at 100 C.","…1 more"],"temperatureC":25,"temperatureK":298.15,"antoineKpa":3.1579292,"antoineMmHg":23.686414,"antoineBar":0.031579292,"magnusKpa":3.161736,"magnusMinusAntoinePct":0.12055,"boilingPointAtAtmosphereC":null,"degraded":false,"notChecked":["accuracy beyond the stated range (Antoine is fitted for 1 to 100 C)","salinity, dissolved gases or non-pure water","…1 more"],"source":"computed locally (Antoine: log10 P[mmHg] = 8.07131 - 1730.63/(233.426 + T), 1-100 C; Magnus: 0.61094 exp(17.625 T/(T + 243.04)) kPa)","asOf":"2026-10-21T06:33:57.390Z","disclaimer":"Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting."}}}},"400":{"description":"A parameter was missing or out of range."},"402":{"description":"Payment Required"},"502":{"description":"The upstream source failed or timed out."}},"x-payment-info":{"price":{"mode":"fixed","currency":"USD","amount":"0.0200"},"protocols":[{"x402":{"network":"eip155:8453","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/saturation-pressure-water"}},{"x402":{"network":"solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/saturation-pressure-water"}},{"x402":{"network":"eip155:137","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/saturation-pressure-water"}},{"x402":{"network":"eip155:42161","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/saturation-pressure-water"}}]}}},"/specific-heat-mixing":{"get":{"operationId":"specific_heat_mixing","summary":"Final temperature of mixed masses (water, ice, steam, solids) with specific heats and water latent heats of fusion and boiling.","description":"Final temperature of mixed masses (water, ice, steam, solids) with specific heats and water latent heats of fusion and boiling.","tags":["calorimetry","specific-heat","latent-heat","mixing"],"parameters":[{"name":"items","in":"query","required":true,"description":"Semicolon list of massKg:substance:tempC. substance is water, ice, steam, a solid name (copper, aluminium, iron, lead, glass, brass, steel, silver, gold) or a specific heat in J/(kg K)","schema":{"type":"string"}}],"responses":{"200":{"description":"The answer.","content":{"application/json":{"schema":{"type":"object","properties":{"verdict":{"type":["null","string"]},"summary":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"finalTemperatureC":{"type":["null","number"]},"state":{"type":["null","string"]},"totalMassKg":{"type":["null","number"]},"waterMassKg":{"type":["null","number"]},"iceRemainingKg":{"type":["null","number"]},"steamKg":{"type":["null","number"]},"totalEnthalpyJ":{"type":["null","number"]},"constants":{"type":["null","object"],"properties":{"cWaterJPerKgK":{"type":["null","number"]},"cIceJPerKgK":{"type":["null","number"]},"cSteamJPerKgK":{"type":["null","number"]},"latentFusionJPerKg":{"type":["null","number"]},"latentVaporisationJPerKg":{"type":["null","number"]}}},"degraded":{"type":["boolean","null"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"source":{"type":["null","string"]},"asOf":{"type":["null","string"]},"disclaimer":{"type":["null","string"]}}},"example":{"verdict":"COMPUTED","summary":"Final temperature 7.53504 C (liquid water) for 0.6 kg mixed.","reasons":["Energy balance with the total enthalpy measured from liquid water at 0 C: ice -334 kJ/kg to melt, steam +2256 kJ/kg to condense released; sum of m x enthalpy is conserved.","The mixture is treated as isolated: no heat to the container or surroundings."],"finalTemperatureC":7.5350374,"state":"liquid water","totalMassKg":0.6,"waterMassKg":0.6,"iceRemainingKg":0,"steamKg":0,"totalEnthalpyJ":18925,"constants":{"cWaterJPerKgK":4186,"cIceJPerKgK":2100,"cSteamJPerKgK":2010,"latentFusionJPerKg":334000,"latentVaporisationJPerKg":2256000},"degraded":false,"notChecked":["heat lost to the container or surroundings (the system is treated as isolated)","phase change of substances other than water (solids are held solid, liquids stay liquid)","…1 more"],"source":"computed locally (energy balance; water 4186 J/(kg K), ice 2100, steam 2010, fusion 334 kJ/kg, vaporisation 2256 kJ/kg)","asOf":"2026-10-21T06:33:57.642Z","disclaimer":"Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting."}}}},"400":{"description":"A parameter was missing or out of range."},"402":{"description":"Payment Required"},"502":{"description":"The upstream source failed or timed out."}},"x-payment-info":{"price":{"mode":"fixed","currency":"USD","amount":"0.0300"},"protocols":[{"x402":{"network":"eip155:8453","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/specific-heat-mixing"}},{"x402":{"network":"solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/specific-heat-mixing"}},{"x402":{"network":"eip155:137","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/specific-heat-mixing"}},{"x402":{"network":"eip155:42161","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/specific-heat-mixing"}}]}}},"/thermal-expansion":{"get":{"operationId":"thermal_expansion","summary":"Linear, area and volume change of a solid for a temperature change, with typical coefficients for common materials.","description":"Linear, area and volume change of a solid for a temperature change, with typical coefficients for common materials.","tags":["thermal-expansion","materials","temperature","engineering"],"parameters":[{"name":"tempFromC","in":"query","required":true,"description":"Starting temperature in degrees C","schema":{"type":"number"}},{"name":"tempToC","in":"query","required":true,"description":"Final temperature in degrees C","schema":{"type":"number"}},{"name":"material","in":"query","required":false,"description":"Material for a typical coefficient: aluminium, brass, copper, steel-carbon, stainless-304, iron, lead, gold, silver, titanium, invar, glass-soda-lime, glass-borosilicate, concrete, pvc, hdpe, acrylic, brick (or send coefficientPerKE6)","schema":{"type":"string"}},{"name":"coefficientPerKE6","in":"query","required":false,"description":"Linear expansion coefficient in 1e-6 per K (e.g. 12 for 12e-6/K); overrides material","schema":{"type":"number"}},{"name":"lengthM","in":"query","required":false,"description":"Original length in metres","schema":{"type":"number"}},{"name":"areaM2","in":"query","required":false,"description":"Original area in m2","schema":{"type":"number"}},{"name":"volumeM3","in":"query","required":false,"description":"Original volume in m3","schema":{"type":"number"}}],"responses":{"200":{"description":"The answer.","content":{"application/json":{"schema":{"type":"object","properties":{"verdict":{"type":["null","string"]},"summary":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"material":{"type":["null","string"]},"linearCoefficientPerK":{"type":["null","number"]},"areaCoefficientPerK":{"type":["null","number"]},"volumeCoefficientPerK":{"type":["null","number"]},"temperatureChangeK":{"type":["null","number"]},"lengthChangeM":{"type":["null","number"]},"lengthChangeMm":{"type":["null","number"]},"finalLengthM":{"type":["null","number"]},"lengthChangePct":{"type":["null","number"]},"degraded":{"type":["boolean","null"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"source":{"type":["null","string"]},"asOf":{"type":["null","string"]},"disclaimer":{"type":["null","string"]}}},"example":{"verdict":"COMPUTED","summary":"steel-carbon (alpha 11.7e-6 per K) over 50 K: length 10 m changes by 5.85 mm.","reasons":["Linear: dL = alpha L dT. Area: dA = 2 alpha A dT. Volume: dV = 3 alpha V dT (isotropic solid).","Coefficient is a typical published value near 20 C; check your alloy.","…1 more"],"material":"steel-carbon","linearCoefficientPerK":0.000011699999999999998,"areaCoefficientPerK":0.000023399999999999996,"volumeCoefficientPerK":0.00003509999999999999,"temperatureChangeK":50,"lengthChangeM":0.00585,"lengthChangeMm":5.85,"finalLengthM":10.00585,"lengthChangePct":0.0585,"degraded":false,"notChecked":["constraint stress when expansion is blocked","coefficients that change with temperature or alloy (values here are typical near 20 C)","…1 more"],"source":"computed locally (dL = alpha L dT; dA = 2 alpha A dT; dV = 3 alpha V dT, with exact (1 + alpha dT)^n forms alongside)","asOf":"2026-10-21T06:33:57.897Z","disclaimer":"Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting."}}}},"400":{"description":"A parameter was missing or out of range."},"402":{"description":"Payment Required"},"502":{"description":"The upstream source failed or timed out."}},"x-payment-info":{"price":{"mode":"fixed","currency":"USD","amount":"0.0200"},"protocols":[{"x402":{"network":"eip155:8453","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/thermal-expansion"}},{"x402":{"network":"solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/thermal-expansion"}},{"x402":{"network":"eip155:137","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/thermal-expansion"}},{"x402":{"network":"eip155:42161","scheme":"exact","currency":"USDC","endpoint":"https://thermo-heat-calc.x402tookit.com/thermal-expansion"}}]}}}}}