Let's break down the problem: **Given:** - Net work done per cycle, \( W_{net} = 418.17 \) kJ/kg - Compression ratio, \( r = 8 \) - Initial pressure, \( P_1 = 100 \) kPa - Initial temperature, \( T_1 = 17^\circ C = 290 \) K **To Find:** - Mean effective pressure (MEP) --- ### **Step 1: Mean Effective Pressure Formula** \[ \text{MEP} = \frac{W_{net}}{v_{max} - v_{min}} \] Where: - \( v_{max} \) = specific volume at the start of compression - \( v_{min} \) = specific volume at the end of compression --- ### **Step 2: Find \( v_{max} \) and \( v_{min} \)** The compression ratio \( r = \frac{v_{max}}{v_{min}} \). From the ideal gas law: \[ v_{max} = \frac{RT_1}{P_1} \] Where \( R \) for air ≈ 0.287 kJ/kg·K. \[ v_{max} = \frac{0.287 \times 290}{100} = \frac{83.23}{100} = 0.8323 \text{ m}^3/\text{kg} \] \[ v_{min} = \frac{v_{max}}{r} = \frac{0.8323}{8} = 0.10404 \text{ m}^3/\text{kg} \] \[ v_{max} - v_{min} = 0.8323 - 0.10404 = 0.72826 \text{ m}^3/\text{kg} \] --- ### **Step 3: Calculate MEP** \[ \text{MEP} = \frac{W_{net}}{v_{max} - v_{min}} = \frac{418.17}{0.72826} = 574.19 \text{ kPa} \] --- ### **Final Answer:** The closest value is **574 kPa**. **Correct option:** - 574 kPa If you need the step-by-step reasoning or have more questions, let me know!