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Related Concept Videos

Equation of State01:07

Equation of State

2.0K
The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and...
2.0K
Path Between Thermodynamics States01:21

Path Between Thermodynamics States

3.5K
Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:
3.5K
Clausius-Clapeyron Equation02:35

Clausius-Clapeyron Equation

59.9K
The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
59.9K
Thermochemical Equations02:55

Thermochemical Equations

31.2K
For a chemical reaction (the system) carried out at constant pressure – with the only work done caused by expansion or contraction – the enthalpy of reaction (also called the heat of reaction, ΔHrxn) is equal to the heat exchanged with the surroundings (qp).
31.2K
Homogeneous Equilibria for Gaseous Reactions02:15

Homogeneous Equilibria for Gaseous Reactions

26.3K
Homogeneous Equilibria for Gaseous Reactions
For gas-phase reactions, the equilibrium constant may be expressed in terms of either the molar concentrations (Kc) or partial pressures (Kp) of the reactants and products. A relation between these two K values may be simply derived from the ideal gas equation and the definition of molarity. According to the ideal gas equation:
26.3K
Van der Waals Equation01:10

Van der Waals Equation

4.7K
The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
4.7K

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High-pressure Sapphire Cell for Phase Equilibria Measurements of CO2/Organic/Water Systems
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Discrimination Between Equations of State.

J Ross Macdonald, Donald R Powell

    Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry
    |December 8, 2021
    PubMed
    Summary
    This summary is machine-generated.

    Analyzing equations of state, this study quantifies how P-V data precision and span discriminate between models. It highlights systematic errors from fitting limited data with incorrect models, crucial for selecting analytical models.

    Keywords:
    Curve fittingdata analysisequations of statemodel discriminationsurface fitting

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    Area of Science:

    • Thermodynamics and Physical Chemistry
    • Materials Science and Engineering

    Background:

    • Equations of state are fundamental for describing material behavior under varying conditions.
    • Selecting the appropriate equation of state is critical for accurate scientific modeling and prediction.
    • Limited experimental data and inherent errors pose challenges in distinguishing between similar equations of state.

    Purpose of the Study:

    • To quantitatively assess the discriminability of different equation pairs using real and synthetic data.
    • To determine the necessary data span and precision for unambiguous discrimination between equations of state.
    • To investigate systematic errors in parameter estimation when fitting limited data with incorrect models.

    Main Methods:

    • Analysis of eight isothermal equations of state.
    • Calculation of discrimination measures based on data span and precision.
    • Utilizing exact synthetic data to evaluate parameter and standard deviation estimation errors.

    Main Results:

    • Quantitative measures for discriminating between equation pairs were derived.
    • Calculated curves illustrate the required P-V data span and precision for unambiguous model selection.
    • Significant systematic errors in parameter and standard deviation estimates were observed when fitting limited data with incorrect models.

    Conclusions:

    • The study provides a framework for assessing the ability to discriminate between equations of state based on experimental data quality.
    • Findings underscore the importance of data span and precision in model selection and highlight potential pitfalls of least squares fitting.
    • Results are applicable to the broader challenge of selecting the optimal analytical model for experimental data.