Cubic equations of state are real-gas models in Thermodynamics II that relate pressure, volume, and temperature with a cubic polynomial in volume. They are used to estimate vapor-liquid equilibrium, fugacity, and phase behavior for non-ideal fluids.
Cubic equations of state are algebraic models in Thermodynamics II that estimate how a real fluid behaves when pressure, temperature, and volume all matter at once. Instead of treating a gas as ideal, they build in non-ideal behavior so you can predict liquid, vapor, and two-phase regions more realistically.
They are called "cubic" because, after rearranging the equation, you get a cubic polynomial in molar volume or compressibility factor. That matters because a cubic equation can have one, two, or three real roots, and those roots can correspond to different physical states. For example, one root may represent the vapor phase, while another may point to a liquid-like state.
The classic examples are the Van der Waals equation, Redlich-Kwong, and Peng-Robinson. These formulas all start from the same idea: real molecules take up space and attract each other, so pressure is not just the simple ideal-gas result. Each model tweaks the attraction and repulsion terms a little differently to improve predictions for different fluids and conditions.
In phase-equilibrium work, a cubic equation of state is more than a P-V-T shortcut. It gives you a way to calculate fugacity coefficients, which then let you check whether a vapor and liquid are in equilibrium. That is why these equations show up in flash calculations, distillation design, and any problem where a substance is near saturation or critical conditions.
A common mistake is treating the cubic equation as if it were only about gas behavior. In Thermodynamics II, the real value is that it connects gas behavior to liquid behavior and phase change. If you know the temperature, pressure, and composition, the equation gives you a practical route to predict whether the fluid is stable as one phase or split into two.
Cubic equations of state show up whenever Thermodynamics II moves from idealized gas laws to real-fluid phase equilibrium. They are the bridge between a simple pressure-volume-temperature relation and the more detailed work of finding saturation conditions, vapor-liquid split, and fugacity.
That makes them central in problems about distillation, flash separation, and mixture behavior. If a mixture is not ideal, you cannot rely on the ideal gas law to estimate phase composition or to decide which phase is favored. A cubic equation gives you the compressibility factor or molar volume you need before you can move on to fugacity calculations.
They also help explain why fluids behave strangely near the critical point. At those conditions, liquid and vapor properties start to blend together, and a real-fluid model has to capture that change in slope and phase stability. The equation is not just a formula to memorize, it is a tool for seeing how intermolecular forces reshape the phase diagram.
If you are solving engineering problems, this term often appears as the first step in a longer chain: choose an equation of state, solve for roots, pick the physically meaningful phase, then calculate fugacity and equilibrium. That chain is a big part of how Thermodynamics II turns theory into process design.
Keep studying Thermodynamics II Unit 10
Visual cheatsheet
view galleryVan der Waals equation
This is the classic starting point for cubic equations of state. It introduces the two big fixes to ideal gas behavior, molecular size and intermolecular attraction, but it is usually too rough for accurate engineering phase-equilibrium work. Seeing it first makes the later cubic models feel like refinements instead of totally new ideas.
Fugacity
Cubic equations of state are often used to calculate fugacity coefficients for real fluids. Once you have fugacity, you can compare phases directly and test vapor-liquid equilibrium. In Thermodynamics II, this is the step that turns a pressure-volume model into a phase-equilibrium tool.
Phase diagram
A cubic equation of state is one way to predict where phase boundaries sit on a phase diagram. It can suggest when a fluid should be liquid, vapor, or a mixture, especially near saturation and the critical region. If you are reading a phase diagram, the equation helps explain why the boundaries curve the way they do.
Critical Pressure
Cubic equations of state are designed to match critical properties more closely than ideal-gas models. Critical pressure is one of the reference points used to tune the attraction and repulsion terms in the equation. That is why these models are often checked against critical data before they are used for mixtures.
A problem set or quiz question usually gives you a fluid, a temperature, a pressure, and maybe a choice of equation of state, then asks you to find the real-fluid state. You may need to solve the cubic form for compressibility factor, pick the physically reasonable root, and decide whether the result corresponds to vapor, liquid, or a two-phase condition. In phase-equilibrium questions, the next step is often calculating fugacity coefficients and checking whether the liquid and vapor fugacities match. A common trap is grabbing the wrong root or assuming there is only one answer because you are used to ideal-gas problems. If the fluid is near saturation, the multiple roots are part of the story, not an error.
Van der Waals is one specific cubic equation of state, while cubic equations of state are the whole family of models that include Van der Waals, Redlich-Kwong, and Peng-Robinson. If a question says "cubic equation of state," it is asking about the general modeling approach, not just the older Van der Waals form.
Cubic equations of state are real-fluid models that relate pressure, volume, and temperature more accurately than the ideal gas law.
They are called cubic because the equation can be rearranged into a cubic polynomial, often in molar volume or compressibility factor.
These models matter most in phase-equilibrium problems, where you need liquid-vapor behavior and fugacity, not just a single gas-phase pressure estimate.
Different roots of the cubic can correspond to different physical states, so choosing the right root is part of the job.
Van der Waals, Redlich-Kwong, and Peng-Robinson are common examples, each with different accuracy tradeoffs.
Cubic equations of state are real-fluid equations that model the relationship between pressure, volume, and temperature with a cubic polynomial. In Thermodynamics II, you use them to estimate phase behavior, especially for vapor-liquid equilibrium and fugacity calculations.
They are called cubic because the equation can be rearranged into a third-degree polynomial in molar volume or compressibility factor. That means the math can produce up to three real roots, which is useful when a fluid may have liquid-like and vapor-like states at the same conditions.
They help you estimate the properties of each phase so you can compute fugacity and check equilibrium conditions. If the vapor and liquid fugacities match, the phases can coexist, which is exactly the kind of step you see in flash calculations and separation problems.
The ideal gas law assumes no intermolecular forces and no molecular volume, so it breaks down for real fluids at higher pressures or near phase change. Cubic equations of state keep the math manageable but add terms that account for attraction and repulsion, so they work better for liquids, vapors, and mixtures.