Question

In Atkin's Chemical Principles: The Quest for Insight, the Clausius inequality is said to be ΔS≥qTΔS≥qTwhere equality applies to a reversible process. Why would the change in entropy be different for a reversible process compared to an irreversible process if entropy is a state function, and the initial and final properties of the system remain the same?

Answer 1

The Clausius inequality shows the difference in entropy change for reversible and irreversible processes. Entropy is a state function and does not depend on the path taken from the initial to the final state. However, additional entropy is produced in an irreversible process due to non-equilibrium effects, leading to a greater overall entropy increase compared to a reversible process.

Step-by-step explanation:

The question you've asked pertains to the Clausius inequality in thermodynamics and why the change in entropy would be different for a reversible process compared to an irreversible one if entropy is a state function. The Clausius inequality is expressed as ΔS≥q/T, where ΔS represents the change in entropy, q is the heat transferred, and T is the temperature.

For a reversible process, the inequality becomes an equality (ΔS=q/T), which indicates that the process occurs without an increase in the entropy of the universe. However, for an irreversible process, the entropy of the universe increases (ΔS>q/T).

Entropy is indeed a state function, meaning that its change depends only on the initial and final states of a system. The confusion arises from the fact that during an irreversible process, additional entropy is generated due to irreversibilities such as friction, turbulence, and other non-equilibrium effects.

This results in a larger increase in entropy when compared to a reversible process that moves through a series of equilibrium states. To calculate the change in entropy for an irreversible process, we conceptually imagine a reversible process that connects the same initial and final states and calculate the entropy change for this hypothetical process. That change will be the same as for the actual irreversible process.

In summary, while entropy as a state function remains unchanged for a given initial and final state, the path taken by a reversible process and an irreversible process can differ significantly in terms of entropy production, thus leading to the disparity in entropy changes observed.