> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Calculate Joule-Thomson Coefficient

> Calculates the Joule-Thomson coefficient μ_JT = (∂T/∂P)_H, which describes the temperature change of a gas during isenthalpic (constant enthalpy) expansion. For real gases, this coefficient can be positive (cooling) or negative (heating) depending on temperature and pressure. The inversion temperature separates these regimes.

**Use Cases:**
- Model non-equilibrium processes in markets
- Analyze expansion/contraction dynamics
- Study irreversible processes in trading
- Temperature-pressure analogies in finance
- Throttling process models

**Formula:** μ_JT = (1/C_p)[T(∂V/∂T)_P - V]

For Van der Waals gas: μ_JT ≈ (2a/RT - b)/C_p

**Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE, Credits: 10]



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/thermodynamics/joule-thomson
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Physics Module
  description: >-
    Physics and Information Theory module for FinceptQuantLib API. Includes
    Shannon/Renyi/Tsallis entropy, KL/JS divergence, mutual information,
    transfer entropy, Fisher information, Boltzmann distribution, Ising model,
    maximum entropy, thermodynamics (free energy, Carnot cycle, van der Waals
    equation), and Maxwell relations. **Pro Tier required. 5 credits per
    request.**
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-physics
    description: Physics and Information Theory module for FinceptQuantLib API
    x-displayName: Physics
paths:
  /quantlib/physics/thermodynamics/joule-thomson:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Joule-Thomson Coefficient
      description: >-
        Calculates the Joule-Thomson coefficient μ_JT = (∂T/∂P)_H, which
        describes the temperature change of a gas during isenthalpic (constant
        enthalpy) expansion. For real gases, this coefficient can be positive
        (cooling) or negative (heating) depending on temperature and pressure.
        The inversion temperature separates these regimes.


        **Use Cases:**

        - Model non-equilibrium processes in markets

        - Analyze expansion/contraction dynamics

        - Study irreversible processes in trading

        - Temperature-pressure analogies in finance

        - Throttling process models


        **Formula:** μ_JT = (1/C_p)[T(∂V/∂T)_P - V]


        For Van der Waals gas: μ_JT ≈ (2a/RT - b)/C_p


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: joule_thomson
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              properties:
                temperature:
                  type: number
                  description: Temperature (Kelvin)
                  default: 300
                  example: 300
                pressure:
                  type: number
                  description: Pressure (Pa)
                  default: 101325
                  example: 101325
                Cp:
                  type: number
                  description: Heat capacity at constant pressure (J/(mol·K))
                  default: 29.1
                  example: 29.1
                a:
                  type: number
                  description: Van der Waals parameter a (Pa·m⁶/mol²)
                  default: 0
                  example: 0.1
                b:
                  type: number
                  description: Van der Waals parameter b (m³/mol)
                  default: 0
                  example: 0.01
            examples:
              ideal_gas:
                summary: Ideal gas (μ_JT = 0)
                value:
                  temperature: 300
                  pressure: 101325
                  Cp: 29.1
                  a: 0
                  b: 0
              real_gas:
                summary: Real gas with Van der Waals corrections
                value:
                  temperature: 300
                  pressure: 101325
                  Cp: 29.1
                  a: 0.137
                  b: 0.000039
      responses:
        '200':
          description: Joule-Thomson coefficient calculated successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      joule_thomson_coefficient:
                        type: number
                        description: >-
                          Joule-Thomson coefficient μ_JT (K/Pa). Positive =
                          cooling on expansion, negative = heating
                        example: 0.00000234
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientCreditsError'
        '422':
          $ref: '#/components/responses/ValidationError'
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientCreditsError:
      description: Insufficient API credits
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Insufficient credits. This endpoint requires 5 credits.
    ValidationError:
      description: Request validation error
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: array
                items:
                  type: object
                  properties:
                    loc:
                      type: array
                      items:
                        type: string
                    msg:
                      type: string
                    type:
                      type: string
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````