δs_universe = δs_system + δs_surroundings

Definition

This equation represents the principle of entropy conservation in a closed system, stating that the change in entropy of the universe ($$δs_{universe}$$) is equal to the sum of the change in entropy of the system ($$δs_{system}$$) and the change in entropy of the surroundings ($$δs_{surroundings}$$). It emphasizes that in any thermodynamic process, the total entropy can either increase or remain constant, but it cannot decrease, reflecting the second law of thermodynamics.

5 Must Know Facts For Your Next Test

1. In an isolated system, $$δs_{universe}$$ is always greater than or equal to zero, confirming that processes naturally progress toward greater disorder.
2. When a system undergoes a reversible process, the change in entropy of the system and surroundings can be calculated precisely, maintaining equilibrium.
3. For irreversible processes, such as spontaneous reactions, $$δs_{universe}$$ increases, highlighting how these processes contribute to overall disorder.
4. The relationship allows for predicting whether a reaction or physical process will occur spontaneously based on the sign of $$δs_{universe}$$.
5. This equation is essential for understanding various thermodynamic processes like phase transitions, chemical reactions, and heat exchanges.

Review Questions

• How does the equation $$δs_{universe} = δs_{system} + δs_{surroundings}$$ help in determining whether a process is spontaneous?
  • The equation indicates that if the total change in entropy of the universe ($$δs_{universe}$$) is positive, the process is spontaneous. This means that for a process to occur naturally, either the entropy of the system or its surroundings (or both) must increase. By calculating $$δs_{system}$$ and $$δs_{surroundings}$$ during a given process, one can evaluate if their sum leads to an increase in entropy, thus determining spontaneity.
• Discuss how reversible and irreversible processes differ in terms of their contributions to entropy based on $$δs_{universe} = δs_{system} + δs_{surroundings}$$.
  • Reversible processes are characterized by changes that can be reversed without any net change in entropy; therefore, both $$δs_{system}$$ and $$δs_{surroundings}$$ can be precisely equalized leading to zero net change in $$δs_{universe}$$. In contrast, irreversible processes lead to an overall increase in $$δs_{universe}$$ as they contribute to greater disorder within both the system and surroundings. This distinction highlights why spontaneous reactions tend to favor irreversible pathways and result in a greater overall increase in entropy.
• Evaluate the implications of $$δs_{universe} = δs_{system} + δs_{surroundings}$$ for real-world applications like chemical reactions and phase changes.
  • The implications of this equation extend to various real-world applications by illustrating how energy dispersal governs chemical reactions and phase changes. For instance, during a chemical reaction, measuring the changes in entropy for both products and reactants can predict reaction spontaneity. Similarly, when ice melts into water, there is an increase in disorder as liquid water has higher entropy than solid ice. Understanding these concepts through $$δs_{universe} = δs_{system} + δs_{surroundings}$$ allows scientists to manipulate conditions for desired outcomes in chemical synthesis and material processing.

Related terms

Entropy: A measure of the disorder or randomness in a system, which increases as energy becomes more dispersed.

Second Law of Thermodynamics: A fundamental principle stating that the total entropy of an isolated system can never decrease over time.

Thermodynamic Equilibrium: A state where a system's macroscopic properties are uniform and unchanging, indicating that entropy is maximized.