One mole of an ideal monatomic gas, occupying 5 L at 3270 °C, is carried through a Carnot cycle. It is first expanded isothermally to a volume of 25 L and then adiabatically to a stage at which the temperature is 270 °C. It is then compressed isothermally to a certain volume and then finally back to the initial state. Calculate the quantities of AE , q and W in each step. Then calculate the efficiency.

Elements Of Electromagnetics
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**Carnot Cycle Problem**

One mole of an ideal monatomic gas, occupying 5 L at 3270 °C, is carried through a Carnot cycle. It is first expanded isothermally to a volume of 25 L and then adiabatically to a stage at which the temperature is 270 °C. It is then compressed isothermally to a certain volume and then finally back to the initial state. Calculate the quantities of ΔE (change in internal energy), q (heat), and W (work) in each step. Then, calculate the efficiency.

**Explanation:**

- **Isothermal Expansion:** The gas expands isothermally from 5 L to 25 L at 3270 °C.
  
- **Adiabatic Expansion:** The gas expands adiabatically until the temperature reaches 270 °C.
  
- **Isothermal Compression:** The gas is compressed isothermally to a certain volume.
  
- **Return to Initial State:** The gas is finally compressed back to the initial state.

The challenge is to determine the changes in internal energy (ΔE), heat (q), and work (W) during each stage of the Carnot cycle, and then calculate the overall efficiency of the cycle.
Transcribed Image Text:**Carnot Cycle Problem** One mole of an ideal monatomic gas, occupying 5 L at 3270 °C, is carried through a Carnot cycle. It is first expanded isothermally to a volume of 25 L and then adiabatically to a stage at which the temperature is 270 °C. It is then compressed isothermally to a certain volume and then finally back to the initial state. Calculate the quantities of ΔE (change in internal energy), q (heat), and W (work) in each step. Then, calculate the efficiency. **Explanation:** - **Isothermal Expansion:** The gas expands isothermally from 5 L to 25 L at 3270 °C. - **Adiabatic Expansion:** The gas expands adiabatically until the temperature reaches 270 °C. - **Isothermal Compression:** The gas is compressed isothermally to a certain volume. - **Return to Initial State:** The gas is finally compressed back to the initial state. The challenge is to determine the changes in internal energy (ΔE), heat (q), and work (W) during each stage of the Carnot cycle, and then calculate the overall efficiency of the cycle.
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