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0.5 mole of an ideal monatomic gas starts from 500 point a in the diagram to the right. It undergoes a constant pressure expansion from a to b; a constant a b 400 volume compression from b to c: and an isothermal 300 compression from c to a. 200 From last week, find the three temperature values Ta, To and T. and the total work for one cycle W. Now find the heat added along the three processes Qab, Qbc and Qca and the efficiency of this process. 100 1 4 Find the change in entropy along each process Sab, volume (m³) pressure (Pa)

0.5 mole of an ideal monatomic gas starts from 500 point a in the diagram to the right. It undergoes a constant pressure expansion from a to b; a constant a b 400 volume compression from b to c: and an isothermal 300 compression from c to a. 200 From last week, find the three temperature values Ta, To and T. and the total work for one cycle W. Now find the heat added along the three processes Qab, Qbc and Qca and the efficiency of this process. 100 1 4 Find the change in entropy along each process Sab, volume (m³) pressure (Pa)

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### Thermodynamic Cycle Analysis of an Ideal Monatomic Gas **Problem Statement:** 0.5 mole of an ideal monatomic gas starts from point \( a \) in the diagram to the right. It undergoes a: - Constant pressure expansion from \( a \) to \( b \); - Constant volume compression from \( b \) to \( c \); - Isothermal compression from \( c \) to \( a \). **Tasks:** 1. **Temperature and Work Calculation:** Using data from last week, find the three temperature values \( T_a \), \( T_b \), and \( T_c \) and the total work for one cycle \( W \). 2. **Heat Added Calculation:** Compute the heat added during the three processes: - \( Q_{ab} \) (from \( a \) to \( b \)) - \( Q_{bc} \) (from \( b \) to \( c \)) - \( Q_{ca} \) (from \( c \) to \( a \)) 3. **Efficiency Calculation:** Determine the efficiency of this thermodynamic process. 4. **Entropy Change:** Find the change in entropy along each process: - \( S_{ab} \) - \( S_{bc} \) - \( S_{ca} \) 5. **Total Entropy Change:** Calculate the total entropy change for the entire cycle. **Graphical Representation:** The accompanying graph depicts the thermodynamic cycle on a Pressure-Volume (P-V) diagram: - **Process \( a \rightarrow b \)**: Constant pressure expansion. - Initial point \( a \): (0.5 m³, 400 Pa) - Final point \( b \): (4 m³, 400 Pa) - **Process \( b \rightarrow c \)**: Constant volume compression. - Initial point \( b \): (4 m³, 400 Pa) - Final point \( c \): (4 m³, 150 Pa) - **Process \( c \rightarrow a \)**: Isothermal compression. - Initial point \( c \): (4 m³, 150 Pa) - Final point \( a \): (0.5 m³, 400 Pa) This graphical analysis will help in understanding the behavior and properties of the gas during different thermodynamic processes. By following these steps and analyzing the cycle, we aim to deepen our understanding
Transcribed Image Text:### Thermodynamic Cycle Analysis of an Ideal Monatomic Gas **Problem Statement:** 0.5 mole of an ideal monatomic gas starts from point \( a \) in the diagram to the right. It undergoes a: - Constant pressure expansion from \( a \) to \( b \); - Constant volume compression from \( b \) to \( c \); - Isothermal compression from \( c \) to \( a \). **Tasks:** 1. **Temperature and Work Calculation:** Using data from last week, find the three temperature values \( T_a \), \( T_b \), and \( T_c \) and the total work for one cycle \( W \). 2. **Heat Added Calculation:** Compute the heat added during the three processes: - \( Q_{ab} \) (from \( a \) to \( b \)) - \( Q_{bc} \) (from \( b \) to \( c \)) - \( Q_{ca} \) (from \( c \) to \( a \)) 3. **Efficiency Calculation:** Determine the efficiency of this thermodynamic process. 4. **Entropy Change:** Find the change in entropy along each process: - \( S_{ab} \) - \( S_{bc} \) - \( S_{ca} \) 5. **Total Entropy Change:** Calculate the total entropy change for the entire cycle. **Graphical Representation:** The accompanying graph depicts the thermodynamic cycle on a Pressure-Volume (P-V) diagram: - **Process \( a \rightarrow b \)**: Constant pressure expansion. - Initial point \( a \): (0.5 m³, 400 Pa) - Final point \( b \): (4 m³, 400 Pa) - **Process \( b \rightarrow c \)**: Constant volume compression. - Initial point \( b \): (4 m³, 400 Pa) - Final point \( c \): (4 m³, 150 Pa) - **Process \( c \rightarrow a \)**: Isothermal compression. - Initial point \( c \): (4 m³, 150 Pa) - Final point \( a \): (0.5 m³, 400 Pa) This graphical analysis will help in understanding the behavior and properties of the gas during different thermodynamic processes. By following these steps and analyzing the cycle, we aim to deepen our understanding
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