EOS Calculator

Category: Physics
- December 06, 2025
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Calculate thermodynamic properties of gases and fluids using various equations of state (EOS). This calculator helps engineers, scientists, and students determine pressure, volume, temperature relationships and derive other thermodynamic properties.

Equation Selection

Fluid Properties

State Variables

kPa
L
Molar volume (volume per mole)
K
mol

Advanced Settings

J/(mol·K)
Will be adjusted based on selected units

Understanding Equations of State

Equations of state (EOS) describe the relationship between pressure, volume, temperature, and quantity of a fluid. They are essential for thermodynamic calculations in chemical engineering, physics, and related fields.

Common Equations of State

Ideal Gas Law: PV = nRT

Van der Waals: (P + a(n/V)²)(V - nb) = nRT

Redlich-Kwong: P = (RT/(V-b)) - (a/(T^(1/2)V(V+b)))

Peng-Robinson: P = (RT/(V-b)) - (a·α(T)/(V²+2bV-b²))

Soave-Redlich-Kwong: P = (RT/(V-b)) - (a·α(T)/(V(V+b)))

Each equation of state has specific applications depending on pressure, temperature, and fluid type.

Compressibility Factor (Z)

The compressibility factor Z = PV/nRT measures deviation from ideal gas behaviour. For ideal gases, Z = 1. Real fluids typically have Z ≠ 1, especially at high pressures or near critical points.

Critical Properties

The critical point represents conditions where liquid and gas phases become indistinguishable. Critical properties (Tc, Pc) are essential parameters in most equations of state and vary by substance.

Disclaimer: This calculator provides estimates based on established thermodynamic equations. Results may vary from experimental data, especially near critical conditions or at extreme pressures. For critical applications, always validate with laboratory measurements or more sophisticated modelling tools.

What is the Equation of State (EOS) Calculator?

The EOS Calculator is a practical tool used to calculate thermodynamic properties of gases and fluids based on established scientific models known as equations of state. It helps users determine relationships between pressure, volume, temperature, and moles of a substance, supporting analyses in engineering, Physics, and chemical processing.

With support for multiple real gas models like Van der Waals, Peng-Robinson, and Ideal Gas Law, this calculator goes beyond simple estimates. It assists in predicting gas behaviour under various conditions, particularly where ideal assumptions fall short.

Ideal Gas Law: PV = nRT

Van der Waals: (P + a(n/V)²)(V - nb) = nRT

Redlich-Kwong: P = (RT/(V - b)) - (a/(T0.5V(V + b)))

Peng-Robinson: P = (RT/(V - b)) - (a·α(T)/(V² + 2bV - b²))

Soave-Redlich-Kwong: P = (RT/(V - b)) - (a·α(T)/(V(V + b)))

Key Features

  • Select from multiple equations of state for accurate modelling.
  • Choose from common fluids or enter custom critical properties.
  • calculate pressure, volume, temperature, or full thermodynamic properties.
  • Supports unit conversions across SI, bar, engineering, and English systems.
  • Displays compressibility factor (Z) and deviation from ideal gas behaviour.
  • Step-by-step equation derivations for deeper understanding.

How to Use the EOS Calculator

  1. Choose an Equation of State: Select from options like Ideal Gas, Van der Waals, or Peng-Robinson.
  2. Pick Calculation Mode: Decide whether you want to calculate pressure, volume, temperature, or properties.
  3. Select a Fluid: Choose a fluid (e.g., methane, oxygen) or enter custom values.
  4. Enter State Variables: Input the known values such as pressure, volume, temperature, and number of moles.
  5. Adjust Advanced Settings: Enable derivation display or adjust the gas constant if needed.
  6. Click "Calculate": View results including primary output, secondary properties, Z-factor, and deviations.

Why This Calculator is Useful

Whether you're working on gas pipeline modelling, designing chemical reactors, or simply learning about gas laws, this tool simplifies complex thermodynamic calculations. It serves as a pressure-volume relationship calculator, a mole and gas behaviour evaluator, and even offers a compressibility factor checker.

In contrast to Other tools like a Work Calculator for job time assessment or a Voltage Drop Calculator for electrical planning, this EOS calculator specialises in thermodynamic fluid properties. It's especially valuable when real gas effects must be considered, similar to how a Heat Index Calculator helps assess perceived temperature due to humidity and heat levels.

Frequently Asked Questions

What is an Equation of State (EOS)?

An EOS is a mathematical model describing the relationship between pressure, volume, temperature, and the amount of gas. It helps predict fluid behaviour under various conditions.

When should I use a real gas equation instead of the Ideal Gas Law?

If your conditions involve high pressures, low temperatures, or the fluid is near its critical point, real gas models like Peng-Robinson or Redlich-Kwong will offer more accurate results.

What does the compressibility factor Z indicate?

Z shows how much a real gas deviates from ideal behaviour. Z = 1 means ideal gas behaviour. Values above or below 1 indicate repulsive or attractive molecular forces.

Can I use this calculator for liquids?

This tool is optimised for gases and supercritical fluids. While some equations support dense phases, results for liquids may be less accurate.

Is this useful for educational purposes?

Yes, the step-by-step derivations and dynamic results make it ideal for learning and understanding gas laws and real gas behaviour.

Conclusion

The EOS Calculator is a helpful resource for students, engineers, and professionals working with gases. It streamlines thermodynamic analysis by offering multiple models and precise results. Whether you're calculating gas pressure or assessing the compressibility factor, this tool helps you make informed decisions in gas and fluid dynamics.