Define Entropy. Write its significance and show that the entropy of a perfect gas remains constant in a reversible process but increase in irreversible process.

ANSWER : Entropy is a fundamental concept in thermodynamics that describes the level of disorder or randomness in a system. It is denoted by the symbol "S." In simple terms, entropy can be thought of as a measure of how spread out or disorganised the particles or energy are within a system.

Significance of Entropy:

Entropy plays a crucial role in understanding the behavior of physical systems, especially in thermodynamics. Here are some key points about its significance:

1. Direction of Processes: Entropy helps us determine the direction in which natural processes occur. In isolated systems, the total entropy tends to increase over time, moving towards a state of maximum disorder, known as thermodynamic equilibrium.

2. Irreversibility: Entropy is closely related to the concept of irreversibility in thermodynamics. Irreversible processes are characterised by an increase in the total entropy of the system and its surroundings, leading to a net increase in disorder.

3. Second Law of Thermodynamics: The increase in entropy over time is stated in the Second Law of Thermodynamics, which is one of the fundamental laws governing the behavior of energy and matter in nature.

Entropy of a Perfect Gas in Reversible and Irreversible Processes:

For a perfect gas, the entropy change in a reversible process and an irreversible process can be described as follows:

1. Reversible Process:

In a reversible process, the system changes its state through a series of infinitesimally small and quasi-static steps. The entropy change for a reversible process can be determined using the formula:

\[ \Delta S_{\text{rev}} = \int{\frac{\delta Q_{\text{rev}}}{T}} \]

where \( \delta Q_{\text{rev}} \) is the infinitesimal amount of heat transferred reversibly to the system, and \( T \) is the temperature of the system in Kelvin.

For a perfect gas, the equation can be simplified as:

\[ \Delta S_{\text{rev}} = \int{\frac{C_v}{T} dT} \]

where \( C_v \) is the molar heat capacity at constant volume.

In a reversible process, the entropy change is path-independent and depends only on the initial and final states of the system. Therefore, the entropy of a perfect gas remains constant in a reversible process.

2. Irreversible Process:

In an irreversible process, the system undergoes changes that are not quasi-static and are not easily reversible. As a result, there are additional dissipative effects that lead to an increase in entropy.

The entropy change for an irreversible process can still be determined using the formula:

\[ \Delta S_{\text{irrev}} = \int{\frac{\delta Q_{\text{irrev}}}{T}} \]

where \( \delta Q_{\text{irrev}} \) is the infinitesimal amount of heat transferred irreversibly to the system.

However, in an irreversible process, the entropy change is greater than that of a reversible process for the same initial and final states. This is because some energy is dissipated as heat during irreversible transformations, leading to a net increase in the system's disorder.

In conclusion, entropy is a crucial concept in thermodynamics that measures the level of disorder in a system. In reversible processes, the entropy of a perfect gas remains constant as the system undergoes changes in a quasi-static manner. On the other hand, in irreversible processes, the entropy of a perfect gas increases due to dissipative effects and the lack of reversibility. This highlights the significance of entropy in understanding the behaviour of physical systems.

Also Read : Write the Definition of Temperature of Inversion.

Also Read : Explain the Joule-Thompson Effect and Derive the Joule-Thompson Coefficient for a real gas.

Connect To Me:

WhatsApp Facebook