Problem 49 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Read the following statement and explanation and answer as per the options given below : Assertion : The heat absorbed during the isothermal expansion of an ideal gas against vacuum is zero. Reason : The volume occupied by the molecules of an ideal gas is zero. (a) If both assertion and reason are CORRECT, and reason is the CORRECT explanation of the assertion. (b) If both assertion and reason are CORRECT, but reason is NOT the CORRECT explanation of the assertion. (c) If assertion is CORRECT, but reason is INCORRECT. (d) If assertion is INCORRECT, but reason is CORRECT.

Step-by-Step Solution

Answer

(b) Both assertion and reason are correct, but reason is not the correct explanation of the assertion.

Step 1: Understand the Assertion

The assertion states that during the isothermal expansion of an ideal gas into a vacuum, the heat absorbed is zero. In thermodynamics, an isothermal process maintains a constant temperature. Expansion into a vacuum implies no opposing pressure (also called a free expansion), meaning no work is done. According to the first law of thermodynamics, in an ideal gas expanding isothermally into a vacuum, the change in internal energy is zero, and thus no heat is absorbed.

Step 2: Analyze the Reason

The reason claims that the volume occupied by the molecules of an ideal gas is zero. In practice, an ideal gas is a theoretical construct where the gas molecules have no volume and there are no interactions between them, which simplifies certain calculations. However, physically, gas molecules do occupy space, but in the ideal gas approximation, their volume is considered negligible.

Step 3: Evaluate the Relation Between Assertion and Reason

The assertion is correct: during an isothermal expansion into a vacuum, no heat is absorbed because no work is done. The reason provided is more related to the definition of an ideal gas rather than explaining why the heat absorbed is zero during expansion into a vacuum. Therefore, while both statements are correct, the reason is not the correct explanation for the assertion.

Step 4: Conclusion

Based on the analysis that both the assertion and the reason are correct statements but do not serve as a correct cause-effect relationship, we select option (b).

Key Concepts

Isothermal Process

In thermodynamics, an isothermal process is a type of process where the temperature remains constant throughout. This means that the heat exchange with the surroundings occurs in such a way that the system does not change its temperature.
To achieve this, the system must be in contact with a thermal reservoir that can supply or absorb heat. For example, during an isothermal expansion of an ideal gas into a vacuum, there is no opposing pressure. This is known as a free expansion.

• Since no work is done in this situation (because there is no external pressure to overcome), the heat added to the system results only in a change in volume but not in temperature, maintaining the energy balance.

When we talk about an ideal gas expanding isothermally into a vacuum, the process is unique because the internal energy change is zero. This directly implies that the heat absorbed or released is zero, as stated by the first law of thermodynamics: \[ \Delta U = Q - W \] where \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system.

Ideal Gas

An ideal gas is a hypothetical concept in physics and chemistry. It's used to simplify the study of gases and their behaviors under various conditions by making assumptions that reduce complexity. The main premise of an ideal gas is that the particles have negligible volume compared to the overall volume of the gas, and there are no intermolecular forces between them.

• This is often expressed through equations such as the ideal gas law: \( PV = nRT \)
• Here, \( P \) stands for pressure, \( V \) is the volume, \( n \) represents the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

While real gases behave similarly to ideal gases under low pressures and high temperatures, deviations occur due to molecular interactions and finite volume.
In the context of isothermal processes, considering a gas as ideal helps in simplifying the calculations, even though, in reality, the actual volume is not zero. The concepts address critical explorations into gas behaviors, leading to necessary approximations in physical calculations.

Free Expansion

Free expansion of a gas refers to its expansion without external work, usually occurring when a gas expands into a vacuum. This idea aligns closely with the concept that no external force or pressure opposes the expansion, meaning work done by the gas is zero.
In a free expansion:

• The process is spontaneous; the gas naturally spreads out due to its internal pressure.
• Since no work is done (as work requires force application over distance), and in an isolated system, no heat is exchanged with the environment, the change in internal energy for an ideal gas remains zero.

This is particularly emphasized in thermodynamics, where free expansion shows that although the volume increases, neither temperature nor internal energy changes. The resultant isothermal expansion into a vacuum confirms zero heat involvement, reinforcing the assertion in the exercise that during such processes, the heat absorbed is zero.
Understanding free expansion is crucial because it illustrates unique scenarios within thermodynamic studies, like adiabatic and isothermal processes, contributing to grasp complexities underlying real-world gas behaviors.