(a) Express the second law of thermodynamics as a...

(a) Express the second law of thermodynamics as a mathematical equation. (b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of $\Delta S_{\text {surr }} ?$ (c) During a certain reversible process, the surroundings undergo an entropy change, $\Delta S_{\text {surr }}=-78 \mathrm{~J} / \mathrm{K}$. What is the entropy change of the system for this process?

Key Concepts

Second Law of Thermodynamics

The second law of thermodynamics states that in any natural (spontaneous) process, the total entropy of an isolated system will either increase or remain constant. Mathematically, it is often expressed as ?Suniv = ?Ssystem + ?Ssurroundings ? 0, where ?Suniv represents the entropy change of the universe. This law helps determine the direction in which processes can occur naturally.

Entropy

Entropy is a measure of the disorder or randomness in a system. It quantifies the number of specific ways a thermodynamic system can be arranged, commonly understood as the degree of disorder. Changes in entropy help predict the spontaneity of a process, with an increase in total entropy typically signifying a spontaneous process.

Spontaneous Process

A spontaneous process is one that occurs without needing to be driven by an external force. In terms of entropy, a spontaneous process is characterized by an overall increase in the entropy of the universe, even if the entropy of the system may decrease, provided that the surroundings compensate by increasing their entropy by a greater amount.

Reversible Process

A reversible process is an idealized thermodynamic process that happens infinitely slowly so that the system remains in thermodynamic equilibrium with its surroundings throughout. In reversible processes, the total entropy change of the universe is zero as any entropy increase in the system is exactly balanced by an entropy decrease in the surroundings, maintaining the overall entropy balance.

System and Surroundings

In thermodynamics, the concept of system and surroundings is used to analyze energy and entropy changes during processes. The system refers to the part of the universe under study, while the surroundings include everything else that can interact with the system. The interplay between the entropy changes in the system and those in the surroundings determines the overall change in the entropy of the universe, which is pivotal in assessing process spontaneity and equilibrium.

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