Carnot efficiency & COP limits API

Computes the maximum reversible thermal efficiency η = 1 − Tc/Th and the Carnot COP for heating (Th/(Th−Tc)) and cooling (Tc/(Th−Tc)) between two reservoir temperatures in Kelvin. Answers 'What is the maximum efficiency of a heat engine?', 'What is the best possible COP for a heat pump?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/carnot-efficiency

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

engineeringthermofluidsthermodynamicscarnotefficiencycopheat-engineheat-pumpsecond-law

API URLhttps://x402.hexl.dev/v1/engineering/carnot-efficiency

Integration docs

Example request

{
  "hotTempK": 600,
  "coldTempK": 300
}

Example response

{
  "hotTempK": 600,
  "coldTempK": 300,
  "thermalEfficiency": 0.5,
  "thermalEfficiencyPercent": 50,
  "carnotCopHeating": 2,
  "carnotCopCooling": 1,
  "formula": "η = 1 - Tc/Th ; COP_heat = Th/(Th-Tc) ; COP_cool = Tc/(Th-Tc)",
  "interpretation": "These are theoretical upper bounds; real machines fall short due to irreversibilities."
}

Input schema

{
  "type": "object",
  "required": [
    "hotTempK",
    "coldTempK"
  ],
  "properties": {
    "hotTempK": {
      "type": "number",
      "description": "hot reservoir temperature (K)",
      "examples": [
        600
      ]
    },
    "coldTempK": {
      "type": "number",
      "description": "cold reservoir temperature (K)",
      "examples": [
        300
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}