> ## 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 Ideal Gas Thermodynamic Properties

> Calculates thermodynamic properties of an ideal gas: entropy and internal energy. The ideal gas model is the simplest thermodynamic system and serves as a baseline for understanding more complex behaviors. Useful for theoretical benchmarks and educational purposes.

**Use Cases:**
- Baseline models for market behavior
- Theoretical efficiency limits
- Educational thermodynamic concepts
- Entropy calculations in simple systems
- Reference values for deviation analysis

**Formulas:**
- S = n C_V ln(T) + n R ln(V) + S_0
- U = n C_V T (for monoatomic: C_V = 3R/2)

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



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/thermodynamics/ideal-gas
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/ideal-gas:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Ideal Gas Thermodynamic Properties
      description: >-
        Calculates thermodynamic properties of an ideal gas: entropy and
        internal energy. The ideal gas model is the simplest thermodynamic
        system and serves as a baseline for understanding more complex
        behaviors. Useful for theoretical benchmarks and educational purposes.


        **Use Cases:**

        - Baseline models for market behavior

        - Theoretical efficiency limits

        - Educational thermodynamic concepts

        - Entropy calculations in simple systems

        - Reference values for deviation analysis


        **Formulas:**

        - S = n C_V ln(T) + n R ln(V) + S_0

        - U = n C_V T (for monoatomic: C_V = 3R/2)


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: ideal_gas
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              properties:
                'n':
                  type: number
                  description: Number of moles
                  default: 1
                  example: 2
                temperature:
                  type: number
                  description: Temperature (Kelvin)
                  default: 300
                  example: 350
                volume:
                  type: number
                  description: Volume (m³)
                  default: 1
                  example: 0.5
                pressure:
                  type: number
                  description: Pressure (Pa) - informational only, not used in calculation
                  default: 101325
                  example: 101325
            examples:
              standard_conditions:
                summary: Standard temperature and pressure
                value:
                  'n': 1
                  temperature: 273.15
                  volume: 0.0224
                  pressure: 101325
              room_temperature:
                summary: Room temperature
                value:
                  'n': 2
                  temperature: 298.15
                  volume: 1
      responses:
        '200':
          description: Ideal gas properties calculated successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      entropy:
                        type: number
                        description: Ideal gas entropy S (J/K)
                        example: 152.34
                      internal_energy:
                        type: number
                        description: Internal energy U (J)
                        example: 8724.5
        '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

````