δs = qrev/t

Definition

The equation δs = qrev/t represents the change in entropy (δs) of a system during a reversible process, where qrev is the heat exchanged reversibly and t is the absolute temperature at which this exchange occurs. This relationship highlights how entropy, a measure of disorder or randomness in a system, increases when heat is added to the system at a specific temperature. Understanding this equation provides insight into the second law of thermodynamics, which asserts that the total entropy of an isolated system can never decrease over time.

5 Must Know Facts For Your Next Test

1. The concept of entropy is crucial for understanding why certain processes are spontaneous; processes tend to occur in the direction that increases total entropy.
2. In a reversible process, the system can be returned to its original state without any net change to the surroundings, maintaining constant entropy.
3. When heat is added to a system at a higher temperature, it contributes more to increasing entropy than heat added at a lower temperature due to the denominator 't' in the equation.
4. The unit of entropy is Joules per Kelvin (J/K), indicating how much energy is dispersed at a specific temperature.
5. Entropy change can also be understood as a measure of energy dispersal; more disorder means more ways to arrange energy states.

Review Questions

• How does the equation δs = qrev/t illustrate the relationship between heat exchange and changes in entropy during a reversible process?
  • The equation δs = qrev/t shows that the change in entropy (δs) is directly related to the heat exchanged reversibly (qrev) and inversely related to temperature (t). This means that for a given amount of heat transferred, increasing the temperature will result in a smaller change in entropy because less disorder is created per unit of heat at higher temperatures. Conversely, at lower temperatures, the same amount of heat transfer leads to a larger increase in entropy, reflecting greater disorder.
• Discuss how the concept of entropy change through δs = qrev/t relates to the second law of thermodynamics and its implications on energy processes.
  • The equation δs = qrev/t is directly tied to the second law of thermodynamics, which states that in any energy exchange, the total entropy of an isolated system can never decrease. This means that all natural processes increase total entropy, supporting the idea that systems tend towards greater disorder. When analyzing reversible processes using this equation, we see that while heat can be exchanged with little impact on total entropy, irreversible processes inevitably lead to an overall increase in entropy, aligning with the second law's implications.
• Evaluate how different temperatures affect entropy changes as described by δs = qrev/t and provide an example illustrating this relationship.
  • Different temperatures play a significant role in determining how much entropy changes when heat is added or removed from a system. At higher temperatures, adding a fixed amount of heat (qrev) results in a smaller increase in entropy (δs) due to the larger value of 't' in the denominator. For example, if you were to add 100 J of heat to water at 100°C versus 10°C, the increase in entropy would be much smaller at 100°C because it's already at a higher energy state. This demonstrates how temperature influences energy dispersal and disorder within systems.

Related terms

Entropy: A thermodynamic property that quantifies the amount of disorder or randomness in a system, often associated with the amount of energy unavailable to do work.

Reversible Process: An idealized process that occurs without any increase in entropy, meaning it can be reversed without leaving any changes in the system or surroundings.

Second Law of Thermodynamics: A fundamental principle stating that in any energy exchange, if no energy enters or leaves a system, the potential energy of the state will always be less than that of the initial state, leading to an increase in entropy.