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Problem 5.8: A dry air parcel undergoes a complete Carnot cycle consisting of the steps indicated in (a)-(d). For each individual step, calculate the mechanical work w (per unit mass) done by the air par- cel and the heat q added to the parcel. allts a) Adiabatic compression from p₁ = 600 hPa and T₁ = 0°C to a temperature T2 of 25°C; -1 Answer: w = -1.8 × 10 J kg¯ b) isothermal expansion to a pressure p3 of 700 hPa; Answer: q = 1.3 x 104 J kg-1 oms c) adiabatic expansion to a temperature T4 of 0°C; htt d) isothermal compression back to the original pressure p₁. giedu. Also, compute shas E e) the total work done and heat added for the complete cycle, and f) the efficiency of the cycle. Ta Hint: You will need to keep track of the state of the parcel at the end of one step to use as the starting point for the next step.

Problem 5.8: A dry air parcel undergoes a complete Carnot cycle consisting of the steps indicated in (a)-(d). For each individual step, calculate the mechanical work w (per unit mass) done by the air par- cel and the heat q added to the parcel. allts a) Adiabatic compression from p₁ = 600 hPa and T₁ = 0°C to a temperature T2 of 25°C; -1 Answer: w = -1.8 × 10 J kg¯ b) isothermal expansion to a pressure p3 of 700 hPa; Answer: q = 1.3 x 104 J kg-1 oms c) adiabatic expansion to a temperature T4 of 0°C; htt d) isothermal compression back to the original pressure p₁. giedu. Also, compute shas E e) the total work done and heat added for the complete cycle, and f) the efficiency of the cycle. Ta Hint: You will need to keep track of the state of the parcel at the end of one step to use as the starting point for the next step.

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**Problem 5.8**: A dry air parcel undergoes a complete Carnot cycle consisting of the steps indicated in (a)–(d). For each individual step, calculate the mechanical work \( w \) (per unit mass) done by the air parcel and the heat \( q \) added to the parcel. a) Adiabatic compression from \( p_1 = 600 \, \text{hPa} \) and \( T_1 = 0^\circ \text{C} \) to a temperature \( T_2 \) of \( 25^\circ \text{C} \);\ **Answer**: \( w = -1.8 \times 10^4 \, \text{J kg}^{-1} \) b) Isothermal expansion to a pressure \( p_3 \) of 700 hPa;\ **Answer**: \( q = 1.3 \times 10^4 \, \text{J kg}^{-1} \) c) Adiabatic expansion to a temperature \( T_4 \) of \( 0^\circ \text{C} \); d) Isothermal compression back to the original pressure \( p_1 \). Also, compute e) the total work done and heat added for the complete cycle, and f) the efficiency of the cycle. **Hint**: You will need to keep track of the state of the parcel at the end of one step to use as the starting point for the next step.
Transcribed Image Text:**Problem 5.8**: A dry air parcel undergoes a complete Carnot cycle consisting of the steps indicated in (a)–(d). For each individual step, calculate the mechanical work \( w \) (per unit mass) done by the air parcel and the heat \( q \) added to the parcel. a) Adiabatic compression from \( p_1 = 600 \, \text{hPa} \) and \( T_1 = 0^\circ \text{C} \) to a temperature \( T_2 \) of \( 25^\circ \text{C} \);\ **Answer**: \( w = -1.8 \times 10^4 \, \text{J kg}^{-1} \) b) Isothermal expansion to a pressure \( p_3 \) of 700 hPa;\ **Answer**: \( q = 1.3 \times 10^4 \, \text{J kg}^{-1} \) c) Adiabatic expansion to a temperature \( T_4 \) of \( 0^\circ \text{C} \); d) Isothermal compression back to the original pressure \( p_1 \). Also, compute e) the total work done and heat added for the complete cycle, and f) the efficiency of the cycle. **Hint**: You will need to keep track of the state of the parcel at the end of one step to use as the starting point for the next step.
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