A general form of equation of state for gases is PV= RT[A+B / V+C / V^2+…], where V is the molar

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A general form of equation of state for gases is PV= RT[A+B...

A general form of equation of state for gases is $\mathrm{PV}=$ $\mathrm{RT}\left[\mathrm{A}+\mathrm{B} / \mathrm{V}+\mathrm{C} / \mathrm{V}^{2}+\ldots\right]$, where $\mathrm{V}$ is the molar volume of the gas and $\mathrm{A}, \mathrm{B}, \mathrm{C} \ldots .$ are constants for the gas. The values of $\mathrm{A}$ and $\mathrm{B}$, if the gas obeys van der Waals equation, are respectively (a) $1, \frac{a}{27 b}$ (b) $1, \mathrm{~b}-\frac{\mathrm{a}}{\mathrm{RT}}$ (c) $\frac{a}{R T}$ (d) $\frac{2 \mathrm{a}}{\mathrm{RT}}$

A general form of equation of state for gases is $\mathrm{PV}=$ $\mathrm{RT}\left[\mathrm{A}+\mathrm{B} / \mathrm{V}+\mathrm{C} / \mathrm{V}^{2}+\ldots\right]$, where $\mathrm{V}$ is the molar
volume of the gas and $\mathrm{A}, \mathrm{B}, \mathrm{C} \ldots .$ are constants for the gas. The values of $\mathrm{A}$ and $\mathrm{B}$, if the gas obeys van der Waals equation, are respectively
(a) $1, \frac{a}{27 b}$
(b) $1, \mathrm{~b}-\frac{\mathrm{a}}{\mathrm{RT}}$
(c) $\frac{a}{R T}$
(d) $\frac{2 \mathrm{a}}{\mathrm{RT}}$

Key Concepts

Virial Coefficients

Virial coefficients are constants in the virial expansion that measure the contributions of molecular interactions to the overall behavior of the gas. The first coefficient typically corresponds to ideal behavior, while subsequent coefficients account for two-body, three-body, and higher order interactions, thereby quantifying deviations from the ideal gas law.

Virial Expansion

The virial expansion is a technique used to express the equation of state as a power series in inverse molar volume. Each term in the series, multiplied by a virial coefficient, represents corrections to ideal gas behavior due to interactions between molecules. This method provides insights into how molecular interactions influence the thermodynamic properties of gases.

Equation of State

An equation of state is a relation that connects the pressure, volume, and temperature of a system, describing its state and behavior under various conditions. It serves as a fundamental tool in thermodynamics for predicting the physical properties of matter, particularly in gases, and is critical for both theoretical studies and practical applications.

van der Waals Equation

The van der Waals equation is a modification of the ideal gas law that includes corrections for the finite size of molecules and the intermolecular forces between them. These corrections, introduced through parameters usually denoted as 'a' for attractive forces and 'b' for the excluded volume, offer a more realistic description of gas behavior, especially under non-ideal conditions.

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