4. Two tenths (kmol) of ideal nitrogen (M=28.01 kg/kmol) in a piston-cylinder assembly undergoes two processes Process 1> 2: constant pressure at 8 bar from V;=2.5 (m³) to V2=1.25 (m³) Process 2 →3: constant volume to pressure of 10 bar Ignoring kinetic and potential effects, find the work done and heat transfer using (i) constant specific heats, and (ii) tables. The value of universal gas constant is 8.314 kJ/kmol.K.

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### Problem Statement

**Objective:**
Calculate the work done and heat transfer for an ideal nitrogen gas in a piston-cylinder assembly undergoing two specific processes.

**Given Data:**
- Quantity of nitrogen gas: 0.2 kmol
- Molar mass of nitrogen (M): 28.01 kg/kmol
- Universal gas constant (R): 8.314 kJ/kmol·K

**Processes:**
1. **Process 1 → 2:** Constant pressure at 8 bar from an initial volume \( V_1 = 2.5 \, \text{m}^3 \) to a final volume \( V_2 = 1.25 \, \text{m}^3 \).
2. **Process 2 → 3:** Constant volume with a change in pressure to 10 bar.

**Assumptions:**
- Ideal gas behavior.
- Kinetic and potential energy changes are negligible.

**Tasks:**
1. Calculate the work done and heat transfer using:
   - (i) Constant specific heats.
   - (ii) Thermodynamic tables.

### Explanation of Processes

- **Constant Pressure Process (1 → 2):**
  - The pressure remains at 8 bar while the volume changes from \(2.5 \, \text{m}^3\) to \(1.25 \, \text{m}^3\).
  - Work done (\( W \)) can be determined using the formula:
    \[
    W = P \times \Delta V
    \]
  - Calculate change in volume (\( \Delta V = V_2 - V_1 \)).

- **Constant Volume Process (2 → 3):**
  - The volume remains constant while the pressure increases to 10 bar.
  - No work is done in this process as work in a closed system is a function of volume change.

By analyzing these processes and using the given data, calculate the respective work and heat transfers for each step using both constant specific heats and reference tables for nitrogen gas.
Transcribed Image Text:### Problem Statement **Objective:** Calculate the work done and heat transfer for an ideal nitrogen gas in a piston-cylinder assembly undergoing two specific processes. **Given Data:** - Quantity of nitrogen gas: 0.2 kmol - Molar mass of nitrogen (M): 28.01 kg/kmol - Universal gas constant (R): 8.314 kJ/kmol·K **Processes:** 1. **Process 1 → 2:** Constant pressure at 8 bar from an initial volume \( V_1 = 2.5 \, \text{m}^3 \) to a final volume \( V_2 = 1.25 \, \text{m}^3 \). 2. **Process 2 → 3:** Constant volume with a change in pressure to 10 bar. **Assumptions:** - Ideal gas behavior. - Kinetic and potential energy changes are negligible. **Tasks:** 1. Calculate the work done and heat transfer using: - (i) Constant specific heats. - (ii) Thermodynamic tables. ### Explanation of Processes - **Constant Pressure Process (1 → 2):** - The pressure remains at 8 bar while the volume changes from \(2.5 \, \text{m}^3\) to \(1.25 \, \text{m}^3\). - Work done (\( W \)) can be determined using the formula: \[ W = P \times \Delta V \] - Calculate change in volume (\( \Delta V = V_2 - V_1 \)). - **Constant Volume Process (2 → 3):** - The volume remains constant while the pressure increases to 10 bar. - No work is done in this process as work in a closed system is a function of volume change. By analyzing these processes and using the given data, calculate the respective work and heat transfers for each step using both constant specific heats and reference tables for nitrogen gas.
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