Problem 168 - Master Resource Book in JEE Main Physics

Question

What is an ideal gas? [a) One that consists of molecules (b) A gas satisfying the assumptions of kinetic theory [c) A gas having Maxwellian distribution of speed (d) A gas consisting of massless particles

Step-by-Step Solution

Answer

(b) A gas satisfying the assumptions of kinetic theory.

Step 1: Understand the concept

An ideal gas is a theoretical gas that perfectly fits all the assumptions of the kinetic molecular theory of gases. This theory assumes that the gas consists of a large number of small particles (molecules or atoms) that are in constant, random motion.

Step 2: Analyze option (a)

Option (a) states that an ideal gas is one that consists of molecules. While real gases do consist of molecules, this alone doesn't define an ideal gas according to kinetic theory.

Step 3: Analyze option (b)

Option (b) mentions a gas satisfying the assumptions of kinetic theory, which directly aligns with the definition of an ideal gas. These assumptions include negligible volume of particles, no intermolecular forces, and perfectly elastic collisions.

Step 4: Analyze option (c)

Option (c) describes a gas having Maxwellian distribution of speed, which describes the statistical distribution of speeds in a gas in equilibrium, important for real gases, but not a defining feature of an ideal gas.

Step 5: Analyze option (d)

Option (d) suggests a gas consisting of massless particles, which is incorrect since ideal gases have mass, even if it's negligible in terms of forces and volume.

Step 6: Conclusion

The ideal gas is best defined as a gas that satisfies all the assumptions of the kinetic theory as stated in option (b). Therefore, the correct option that describes an ideal gas is (b).

Key Concepts

Kinetic Molecular Theory

The Kinetic Molecular Theory is a fundamental concept in understanding gases and their behavior. It provides an idealized picture of how gas molecules move and interact. The core ideas of this theory include:

• Gases are composed of a large number of small particles, either molecules or atoms.
• These particles are in constant, random motion, colliding with each other and the walls of their container.
• The particles are so small compared to the distances between them that their volume is negligible.
• There are no intermolecular forces exerted between the gas particles except during collisions.
• All collisions between gas molecules are perfectly elastic, meaning kinetic energy is conserved.

This theory helps explain various gas laws and predictions about gas behavior under different conditions. By understanding these foundational principles, we can better grasp how real gases might deviate from this ideal behavior due to factors like intermolecular forces or the actual size of the molecules.

Maxwellian Distribution

The Maxwellian Distribution, named after James Clerk Maxwell, is crucial for understanding the range of speeds in a gas sample at equilibrium. It is important to note that not all molecules in a gas move at the same speed. The key points include:

• The distribution describes how molecular speeds are spread out within a gas. Many molecules may have moderate speeds while fewer will have very high or very low speeds.
• This distribution changes with temperature. As temperature increases, the distribution shifts so that more molecules have higher speeds.
• It is an important concept for real gases, particularly because it provides a statistical approach which aligns more with observable behaviors in real-world scenarios.

Although the Maxwellian Distribution is applicable to real gases, it serves as a bridge to understanding deviations from the ideal assumptions, especially under different temperatures and pressures.

Assumptions of Kinetic Theory

To fully understand what defines an ideal gas, it's critical to explore the assumptions of the kinetic theory, which the concept is based on. These assumptions include:

• Gas particles are point masses; they occupy no space.
• All motion is perfectly random and continuous.
• No intermolecular forces act between these particles outside of collisions.
• Collisions between molecules and with the walls of the container are perfectly elastic.
• Gas particles move in straight lines between collisions.

These assumptions simplify calculations and predictions, making models derived from this theory a useful approximation in many scenarios. In practice, real gases may deviate from these assumptions because molecules have finite volume, exhibit interaction forces, and their collisions are not always perfectly elastic. Nevertheless, understanding these ideal conditions helps in differentiating how and why real gases behave differently under varying conditions.

Real vs Ideal Gas

Understanding the differences between real and ideal gases is fundamental in predicting gas behavior under various conditions. Some of the primary differences include:

• In an ideal gas, particle volume and intermolecular forces are neglected, but in real gases, these factors are significant, especially at high pressures and low temperatures.
• Real gases may condense into liquids or solids when cooled, while ideal gases do not exhibit phase changes.
• The behavior of real gases often deviates from that predicted by ideal gas laws due to the influences of molecular interactions and actual particle volumes.

By studying ideal gas laws, scientists and students can develop formulas and models, but they must incorporate factors like van der Waals forces to accurately describe real gas behavior. Thus, recognizing the conditions under which gases diverge from ideal behavior is essential for applications such as chemical engineering, physics, and environmental science.