Air undergoes two processes in series: Process 1-2: Process 2-3: Polytropic compression, with n = 1.2, from P₁ = 140 kPa, V₁ = 0.8 m² to V₂ = .04 m³ Constant pressure process to V₁ = V₁ Sketch the process the process on a P-V diagram and determine the work from Process 1-3.
Air undergoes two processes in series: Process 1-2: Process 2-3: Polytropic compression, with n = 1.2, from P₁ = 140 kPa, V₁ = 0.8 m² to V₂ = .04 m³ Constant pressure process to V₁ = V₁ Sketch the process the process on a P-V diagram and determine the work from Process 1-3.
Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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![### Thermodynamic Processes of Air
Air undergoes two processes in series:
#### Process 1-2:
- **Type:** Polytropic compression
- **Polytropic index (n):** 1.2
- **Initial pressure (P1):** 140 kPa
- **Initial volume (V1):** 0.8 m³
- **Final volume (V2):** 0.04 m³
#### Process 2-3:
- **Type:** Constant pressure process
- **Final volume (V3):** V₁ (= 0.8 m³)
### Task:
- Sketch the process on a Pressure-Volume (P-V) diagram.
- Determine the work done from Process 1 to Process 3.
### Detailed Guide:
1. **P-V Diagram Sketch:**
- **Process 1-2** will be a curve showing the polytropic compression from (P1, V1) = (140 kPa, 0.8 m³) to (P2, V2) on the P-V diagram. Since it's a compression, the curve should slope downwards.
- **Process 2-3** will be a horizontal line moving from V2 back to V1, indicating a constant pressure process.
2. **Determine the Work Done:**
- **For Process 1-2 (Polytropic Process):**
\[
W_{1-2} = \frac{P_1 V_1 - P_2 V_2}{1 - n}
\]
- **For Process 2-3 (Constant Pressure):**
\[
W_{2-3} = P_3 (V_3 - V_2)
\]
- **Total Work (W):**
\[
W_{total} = W_{1-2} + W_{2-3}
\]
Make sure to substitute the known values into the formulas to calculate the specific work done in each process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf82ec8f-02f7-492b-b62b-f53ab94e90b9%2Fe1ee7dc4-f0dd-4cbf-884c-db0af139fa8a%2Fcjiyzcg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Thermodynamic Processes of Air
Air undergoes two processes in series:
#### Process 1-2:
- **Type:** Polytropic compression
- **Polytropic index (n):** 1.2
- **Initial pressure (P1):** 140 kPa
- **Initial volume (V1):** 0.8 m³
- **Final volume (V2):** 0.04 m³
#### Process 2-3:
- **Type:** Constant pressure process
- **Final volume (V3):** V₁ (= 0.8 m³)
### Task:
- Sketch the process on a Pressure-Volume (P-V) diagram.
- Determine the work done from Process 1 to Process 3.
### Detailed Guide:
1. **P-V Diagram Sketch:**
- **Process 1-2** will be a curve showing the polytropic compression from (P1, V1) = (140 kPa, 0.8 m³) to (P2, V2) on the P-V diagram. Since it's a compression, the curve should slope downwards.
- **Process 2-3** will be a horizontal line moving from V2 back to V1, indicating a constant pressure process.
2. **Determine the Work Done:**
- **For Process 1-2 (Polytropic Process):**
\[
W_{1-2} = \frac{P_1 V_1 - P_2 V_2}{1 - n}
\]
- **For Process 2-3 (Constant Pressure):**
\[
W_{2-3} = P_3 (V_3 - V_2)
\]
- **Total Work (W):**
\[
W_{total} = W_{1-2} + W_{2-3}
\]
Make sure to substitute the known values into the formulas to calculate the specific work done in each process.
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