Step 1: Understanding the Question: The goal is to compare the magnitude of work done in irreversible isothermal expansion and compression processes involving single and multiple steps. Step 2: Key Formula or Approach: 1. Work is the area under the P-V curve. 2. For expansion: \(|W_{\text{reversible}}|>|W_{\text{multistep}}|>|W_{\text{single-step}}|\). 3. For compression: \(|W_{\text{single-step}}|>|W_{\text{multistep}}|>|W_{\text{reversible}}|\). Step 3: Detailed Explanation: - In expansion, the system does work against an external pressure. A multi-step expansion (I) stays closer to the isotherm, covering more area under the curve than a single-step expansion (II), where the system immediately works against the lower final pressure. Hence, \(|W_1|>|W_2|\). - In compression, work is done on the system. In a single-step compression (III), you immediately apply the maximum final pressure, resulting in the largest possible area. In multi-step compression (IV), you increase pressure gradually, reducing the "excess" work required. Hence, \(|W_3|>|W_4|\). - Comparing expansion vs compression between the same volume limits: the compression work (work done on the gas) is always greater than the expansion work (work done by the gas). Therefore, the combined order of magnitudes is: \(|W_2|<|W_1|<|W_4|<|W_3|\). Step 4: Final Answer: The correct magnitude order is \(|W_2|<|W_1|<|W_4|<|W_3|\).
