Let's break down the problem and solve it step by step: **Given:** - Net work done per cycle, \( W_{net} = 418.17 \) kJ/kg - Compression ratio, \( r = 8 \) - Initial conditions: \( P_1 = 100 \) kPa, \( T_1 = 17^\circ C = 290 \) K **Asked:** Calculate the mean effective pressure (MEP) for this cycle. --- ### Step 1: Formula for Mean Effective Pressure (MEP) The mean effective pressure is given by: \[ MEP = \frac{W_{net}}{v_{max} - v_{min}} \] Where: - \( W_{net} \) = net work per cycle (kJ/kg) - \( v_{max} \) = specific volume at the beginning of the compression stroke (m³/kg) - \( v_{min} \) = specific volume at the end of the compression stroke (m³/kg) But \( v_{min} = v_{max}/r \), so: \[ MEP = \frac{W_{net}}{v_{max} - v_{max}/r} = \frac{W_{net}}{v_{max} (1 - 1/r)} \] --- ### Step 2: Find \( v_{max} \) Use the ideal gas law: \[ v_{max} = \frac{RT_1}{P_1} \] Where: - \( R \) (for air) \( = 0.287 \) kJ/kg·K - \( T_1 = 290 \) K - \( P_1 = 100 \) kPa \[ v_{max} = \frac{0.287 \times 290}{100} = \frac{83.23}{100} = 0.8323 \text{ m}^3/\text{kg} \] --- ### Step 3: Substitute values \[ MEP = \frac{418.17}{0.8323 \left(1 - \frac{1}{8}\right)} \] \[ 1 - \frac{1}{8} = \frac{7}{8} = 0.875 \] \[ MEP = \frac{418.17}{0.8323 \times 0.875} \] \[ = \frac{418.17}{0.7270} \] \[ = 575 \text{ kPa} \] --- ### Step 4: Match with options Closest option: **574 kPa** --- **Final Answer:** \[ \boxed{574 \text{ kPa}} \]