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Question

Real gases follow _______.

The correct answer is

Van der Waals equation of state

Let's analyze the behavior of real gases and compare it with the options provided.

Understanding Real Gases vs. Ideal Gases

The ideal gas law, given by the equation $\text{PV} = \text{nRT}$, is a simple model that describes the behavior of hypothetical ideal gases. An ideal gas is assumed to consist of point particles that do not interact with each other except during perfectly elastic collisions, and the volume occupied by the gas molecules themselves is considered negligible compared to the volume of the container.

However, real gases are different from ideal gases. In real gases:

  • Gas molecules have a finite volume.
  • There are attractive and repulsive forces between gas molecules (intermolecular forces).

These differences become significant at high pressures (where molecules are close together and their volume becomes comparable to the container volume) and low temperatures (where intermolecular forces become more dominant). Therefore, real gases do not perfectly follow the ideal gas law under all conditions.

Why Real Gases Follow the Van der Waals Equation

Because real gases deviate from ideal behavior, a more accurate equation of state is needed to describe their properties. The Van der Waals equation is one such equation, developed by Johannes Diderik van der Waals. It modifies the ideal gas law by introducing two correction terms:

  1. A correction for the finite volume of the molecules.
  2. A correction for the attractive intermolecular forces.

The Van der Waals equation of state is typically written as:

$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$

Where:

  • $P$ is the pressure of the gas.
  • $V$ is the volume of the container.
  • $n$ is the number of moles of gas.
  • $T$ is the absolute temperature.
  • $R$ is the ideal gas constant.
  • $a$ is a constant that accounts for the attractive intermolecular forces.
  • $b$ is a constant that accounts for the volume occupied by the gas molecules themselves.

The constants $a$ and $b$ are specific to each gas.

Analyzing the Other Options

  • Newton’s law: Newton's laws describe motion and forces. While the motion of gas particles can be analyzed using Newtonian mechanics, Newton's laws themselves are not an equation of state describing the macroscopic behavior (like pressure, volume, temperature relationship) of gases.
  • Gay-Lussac’s law: This law states that for a fixed mass of gas at constant volume, the pressure is directly proportional to its absolute temperature ($P \propto T$ at constant $V$ and $n$). This is derived from the ideal gas law and describes ideal gas behavior.
  • Charles’s law: This law states that for a fixed mass of gas at constant pressure, the volume is directly proportional to its absolute temperature ($V \propto T$ at constant $P$ and $n$). This is also derived from the ideal gas law and describes ideal gas behavior.

Both Gay-Lussac's law and Charles's law are part of the empirical gas laws that led to the ideal gas law, and they are accurate only for ideal gases or real gases behaving ideally (e.g., at low pressure and high temperature).

Therefore, among the given options, the Van der Waals equation of state is specifically designed to describe the behavior of real gases, accounting for their deviations from ideality.

Equation/Law Describes
Ideal Gas Law ($PV=nRT$) Ideal gases (hypothetical)
Van der Waals Equation Real gases (with corrections)
Gay-Lussac's Law Ideal gases (P-T relationship at constant V)
Charles's Law Ideal gases (V-T relationship at constant P)
Newton's Laws Motion and forces (not gas state equation)

Based on the analysis, real gases are best described by the Van der Waals equation of state among the given choices.

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Important Questions from Ideal and Real Gases

  1. A perfect gas at 25°C is heated at constant pressure till its volume is doubled. The final temperature will be-

  2. Which of the following laws states that the volume of a gas is inversely proportional to the pressure of a gas?

  3. The internal energy of a perfect gas does not change during the-

  4. The ratio of specific heat of air at constant pressure to the specific heat of air at constant volume is equal to -

  5. A gas having a negative Joule-Thompson effect (μ < 0), when throttled will

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