Suppose that two systems, each composed of two particles rep- resented by circles, have 20 J of total energy. Which system, A or B, has the greatest entropy? Why? System A 10J System B 12J 8 J

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**Transcription and Explanation for Educational Website**

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**Problem Context:**

29. Suppose that two systems, each composed of two particles represented by circles, have 20 J of total energy. Which system, A or B, has the greatest entropy? Why?

**Diagram Explanation:**

- *System A:* 
  - One particle is associated with 10 J of energy.
  - The second particle is also associated with 10 J of energy.
  
- *System B:*
  - One particle is associated with 12 J of energy.
  - The second particle is associated with 8 J of energy.

**Analysis:**

Entropy is a measure of the number of ways energy can be distributed among the particles in a system. In general, entropy is higher when energy is spread out more evenly among the particles.

- *System A:* The energy distribution is equal between both particles (10 J each).
  
- *System B:* The energy distribution is unequal (12 J and 8 J).

**Conclusion:**

System A has a more even distribution of energy, with each particle having 10 J. Therefore, System A likely has the greater entropy because the energy is more evenly distributed, leading to more possible microstates or configurations.

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This is a conceptual analysis and the idea of entropy in thermodynamics relates to the number of configurations or microstates available to a system, often leading to higher entropy with more even distributions of energy.
Transcribed Image Text:**Transcription and Explanation for Educational Website** --- **Problem Context:** 29. Suppose that two systems, each composed of two particles represented by circles, have 20 J of total energy. Which system, A or B, has the greatest entropy? Why? **Diagram Explanation:** - *System A:* - One particle is associated with 10 J of energy. - The second particle is also associated with 10 J of energy. - *System B:* - One particle is associated with 12 J of energy. - The second particle is associated with 8 J of energy. **Analysis:** Entropy is a measure of the number of ways energy can be distributed among the particles in a system. In general, entropy is higher when energy is spread out more evenly among the particles. - *System A:* The energy distribution is equal between both particles (10 J each). - *System B:* The energy distribution is unequal (12 J and 8 J). **Conclusion:** System A has a more even distribution of energy, with each particle having 10 J. Therefore, System A likely has the greater entropy because the energy is more evenly distributed, leading to more possible microstates or configurations. --- This is a conceptual analysis and the idea of entropy in thermodynamics relates to the number of configurations or microstates available to a system, often leading to higher entropy with more even distributions of energy.
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