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### Entropy Changes in the Carnot Cycle In this exercise, we will explore the concept of entropy changes in the context of the Carnot cycle. The aim is to express the entropy changes of the hot reservoir, the cold reservoir, and the universe using the given variables: \(Q_H\), \(T_H\), \(Q_C\), and \(T_C\). #### Diagram Explanation The problem includes two illustrations: 1. **Pressure-Volume (P-V) Diagram**: This graph displays the Carnot cycle's four main processes (M-N-P-O) through which a working substance is cycled. The arrows indicate the direction of heat flow: - \(Q_H\): Heat absorbed from the hot reservoir (at point M to N). - \(Q_C\): Heat rejected to the cold reservoir (at point P to O). 2. **Schematic Diagram**: This shows the heat exchange between the hot reservoir (top, at temperature \(T_H\)), the Carnot engine (middle), and the cold reservoir (bottom, at temperature \(T_C\)). The work done by the engine is represented by \(W\). #### Steps to Enter Mathematical Answers - Use the math type box to enter your answer in terms of \(Q_H\), \(T_H\), \(Q_C\), and \(T_C\). - For entering subscripts, follow the guide provided (illustrated in the given image with the MathType editor). #### Important Notes - Subscripts are case-sensitive. ### Questions 1. **Entropy change of the hot reservoir \((\Delta S_H)\)** \(\Delta S_H = \) 2. **Entropy change of the cold reservoir \((\Delta S_C)\)** \(\Delta S_C = \) 3. **Entropy change of the universe (Carnot engine + hot reservoir + cold reservoir) \((\Delta S_U)\)** \(\Delta S_U = \) Refer to the provided fields and ensure correct, case-sensitive answers: - a) Entropy change of the hot reservoir: \(\Delta S_H = \_\_\_\) - b) Entropy change of the cold reservoir: \(\Delta S_C = \_\_\_\) - c) Entropy change of the universe: \(\Delta S_U = \_\_\_\)

### Entropy Changes in the Carnot Cycle In this exercise, we will explore the concept of entropy changes in the context of the Carnot cycle. The aim is to express the entropy changes of the hot reservoir, the cold reservoir, and the universe using the given variables: \(Q_H\), \(T_H\), \(Q_C\), and \(T_C\). #### Diagram Explanation The problem includes two illustrations: 1. **Pressure-Volume (P-V) Diagram**: This graph displays the Carnot cycle's four main processes (M-N-P-O) through which a working substance is cycled. The arrows indicate the direction of heat flow: - \(Q_H\): Heat absorbed from the hot reservoir (at point M to N). - \(Q_C\): Heat rejected to the cold reservoir (at point P to O). 2. **Schematic Diagram**: This shows the heat exchange between the hot reservoir (top, at temperature \(T_H\)), the Carnot engine (middle), and the cold reservoir (bottom, at temperature \(T_C\)). The work done by the engine is represented by \(W\). #### Steps to Enter Mathematical Answers - Use the math type box to enter your answer in terms of \(Q_H\), \(T_H\), \(Q_C\), and \(T_C\). - For entering subscripts, follow the guide provided (illustrated in the given image with the MathType editor). #### Important Notes - Subscripts are case-sensitive. ### Questions 1. **Entropy change of the hot reservoir \((\Delta S_H)\)** \(\Delta S_H = \) 2. **Entropy change of the cold reservoir \((\Delta S_C)\)** \(\Delta S_C = \) 3. **Entropy change of the universe (Carnot engine + hot reservoir + cold reservoir) \((\Delta S_U)\)** \(\Delta S_U = \) Refer to the provided fields and ensure correct, case-sensitive answers: - a) Entropy change of the hot reservoir: \(\Delta S_H = \_\_\_\) - b) Entropy change of the cold reservoir: \(\Delta S_C = \_\_\_\) - c) Entropy change of the universe: \(\Delta S_U = \_\_\_\)

Physics for Scientists and Engineers
Physics for Scientists and Engineers
10th Edition
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter21: Heat Engines, Entropy, And The Second Law Of Thermodynamics
Section: Chapter Questions
Problem 38AP: A system consisting of n moles of an ideal gas with molar specific heat at constant pressure Cr...
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### Entropy Changes in the Carnot Cycle In this exercise, we will explore the concept of entropy changes in the context of the Carnot cycle. The aim is to express the entropy changes of the hot reservoir, the cold reservoir, and the universe using the given variables: \(Q_H\), \(T_H\), \(Q_C\), and \(T_C\). #### Diagram Explanation The problem includes two illustrations: 1. **Pressure-Volume (P-V) Diagram**: This graph displays the Carnot cycle's four main processes (M-N-P-O) through which a working substance is cycled. The arrows indicate the direction of heat flow: - \(Q_H\): Heat absorbed from the hot reservoir (at point M to N). - \(Q_C\): Heat rejected to the cold reservoir (at point P to O). 2. **Schematic Diagram**: This shows the heat exchange between the hot reservoir (top, at temperature \(T_H\)), the Carnot engine (middle), and the cold reservoir (bottom, at temperature \(T_C\)). The work done by the engine is represented by \(W\). #### Steps to Enter Mathematical Answers - Use the math type box to enter your answer in terms of \(Q_H\), \(T_H\), \(Q_C\), and \(T_C\). - For entering subscripts, follow the guide provided (illustrated in the given image with the MathType editor). #### Important Notes - Subscripts are case-sensitive. ### Questions 1. **Entropy change of the hot reservoir \((\Delta S_H)\)** \(\Delta S_H = \) 2. **Entropy change of the cold reservoir \((\Delta S_C)\)** \(\Delta S_C = \) 3. **Entropy change of the universe (Carnot engine + hot reservoir + cold reservoir) \((\Delta S_U)\)** \(\Delta S_U = \) Refer to the provided fields and ensure correct, case-sensitive answers: - a) Entropy change of the hot reservoir: \(\Delta S_H = \_\_\_\) - b) Entropy change of the cold reservoir: \(\Delta S_C = \_\_\_\) - c) Entropy change of the universe: \(\Delta S_U = \_\_\_\)
Transcribed Image Text:### Entropy Changes in the Carnot Cycle In this exercise, we will explore the concept of entropy changes in the context of the Carnot cycle. The aim is to express the entropy changes of the hot reservoir, the cold reservoir, and the universe using the given variables: \(Q_H\), \(T_H\), \(Q_C\), and \(T_C\). #### Diagram Explanation The problem includes two illustrations: 1. **Pressure-Volume (P-V) Diagram**: This graph displays the Carnot cycle's four main processes (M-N-P-O) through which a working substance is cycled. The arrows indicate the direction of heat flow: - \(Q_H\): Heat absorbed from the hot reservoir (at point M to N). - \(Q_C\): Heat rejected to the cold reservoir (at point P to O). 2. **Schematic Diagram**: This shows the heat exchange between the hot reservoir (top, at temperature \(T_H\)), the Carnot engine (middle), and the cold reservoir (bottom, at temperature \(T_C\)). The work done by the engine is represented by \(W\). #### Steps to Enter Mathematical Answers - Use the math type box to enter your answer in terms of \(Q_H\), \(T_H\), \(Q_C\), and \(T_C\). - For entering subscripts, follow the guide provided (illustrated in the given image with the MathType editor). #### Important Notes - Subscripts are case-sensitive. ### Questions 1. **Entropy change of the hot reservoir \((\Delta S_H)\)** \(\Delta S_H = \) 2. **Entropy change of the cold reservoir \((\Delta S_C)\)** \(\Delta S_C = \) 3. **Entropy change of the universe (Carnot engine + hot reservoir + cold reservoir) \((\Delta S_U)\)** \(\Delta S_U = \) Refer to the provided fields and ensure correct, case-sensitive answers: - a) Entropy change of the hot reservoir: \(\Delta S_H = \_\_\_\) - b) Entropy change of the cold reservoir: \(\Delta S_C = \_\_\_\) - c) Entropy change of the universe: \(\Delta S_U = \_\_\_\)
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