Question

For given four processes compare magnitude of work:

• A. \( |W_1|>|W_2|>|W_3|>|W_4| \)
• B. \( |W_1|<|W_2|<|W_3|<|W_4| \)
• C. \( |W_1|<|W_3|<|W_2|<|W_4| \)
• D. \( |W_2|<|W_1|<|W_4|<|W_3| \)

Answer 1

The Correct Option is D

Step 1: Work in thermodynamic processes.
In thermodynamics, the work done during an expansion or compression process is related to the pressure-volume relationship. The work done in an isothermal process depends on whether the process is single-step or multi-step, and also whether the process involves expansion or compression.
Step 2: Comparison of processes.
- (I) Isothermal multistep expansion (W\(_1\)): The work done in a multi-step expansion process is generally larger than in a single-step process, due to the gradual increase in volume.
- (II) Isothermal single-step expansion (W\(_2\)): In a single-step expansion, the work is smaller compared to a multistep expansion.
- (III) Isothermal single-step compression (W\(_3\)): In a single-step compression, the work done is smaller compared to a multistep compression.
- (IV) Isothermal multi-step compression (W\(_4\)): The work done in a multi-step compression process is larger than in a single-step compression process.

Step 3: Conclusion.
Thus, the correct comparison of magnitudes of work is given by option (4), where \(| W_2 |<| W_1 |<| W_4 |<| W_3 |\).
Final Answer: (4) \(| W_2 |<| W_1 |<| W_4 |<| W_3 |\)