Let's break down the problem: **Given:** - Net work done (\( W_{net} \)) = 418.17 kJ/kg (assume magnitude, as work done by the cycle is positive) - Compression ratio (\( r \)) = 8 - Initial temperature (\( T_1 \)) = 17°C = 290 K - Initial pressure (\( P_1 \)) = 100 kPa **Asked:** Mean effective pressure (MEP) ### Step 1: Find the Specific Volume at the Start of Compression (\( v_1 \)) From the ideal gas law: \[ P_1 v_1 = R T_1 \] For air, \( R = 0.287 \) kJ/kg·K \[ v_1 = \frac{R T_1}{P_1} \] \[ v_1 = \frac{0.287 \times 290}{100} \] \[ v_1 = \frac{83.23}{100} = 0.8323 \text{ m}^3/\text{kg} \] ### Step 2: Calculate the Displacement Volume For 1 kg of air, the displacement volume is: \[ v_{displacement} = v_1 \left(1 - \frac{1}{r}\right) \] \[ = 0.8323 \left(1 - \frac{1}{8}\right) = 0.8323 \times 0.875 = 0.728 \text{ m}^3/\text{kg} \] ### Step 3: Mean Effective Pressure (MEP) Formula \[ MEP = \frac{W_{net}}{v_{displacement}} \] \[ MEP = \frac{418.17}{0.728} = 574.4 \text{ kPa} \] ### Step 4: Choose the Closest Option - 745 kPa - 475 kPa - 547 kPa - **574 kPa** ← **This is the correct answer** --- **Final Answer:** The mean effective pressure is **574 kPa**.