Question

Why does a nonquasi-equilibrium expansion process deliver less work than the corresponding quasi-equilibrium one?

Short answer

Answer: A nonquasi-equilibrium expansion process delivers less work than a quasi-equilibrium expansion process because it does not maintain mechanical equilibrium throughout the process. The rapid and uneven changes in pressure and temperature inside the system lead to a less efficient distribution of energy and ultimately result in a lower work output. Quasi-equilibrium expansion processes, on the other hand, maintain mechanical equilibrium by going through a series of infinitesimally small intermediate states, allowing for a controlled and efficient distribution of energy and work.

Step-by-step solution

Understand nonquasi-equilibrium expansion processes

Nonquasi-equilibrium expansion processes occur rapidly and don't allow enough time for the system to adjust to external changes and maintain mechanical equilibrium. In these cases, the pressure and temperature inside the system can vary throughout the expansion process, which leads to an uneven and less efficient distribution of energy and work.

Understand quasi-equilibrium expansion processes

In a quasi-equilibrium expansion process, the system goes through a series of infinitesimally small intermediate states, each with a uniform and well-defined pressure and temperature. This allows the system to maintain mechanical equilibrium throughout the process, and the work done in each step contributes to the total work output in a controlled and efficient manner.

Comparing work output

From the first law of thermodynamics, the work done during an expansion process can be expressed as W = -\int_{V1}^{V2} P dV, where W is the work done, P is the pressure of the system, and V1 and V2 are the initial and final volumes, respectively. In a quasi-equilibrium expansion process, the pressure P can be replaced with the external pressure P_{ext}, as they are nearly equal due to the slow, controlled nature of the expansion. For the nonquasi-equilibrium expansion process, however, the pressure is not equal to the external pressure throughout the process, and the pressure changes unevenly and unpredictably. This results in the work done being less efficient and ultimately producing a lower work output.

Conclusion

Nonquasi-equilibrium expansion processes deliver less work than the corresponding quasi-equilibrium ones because they do not maintain mechanical equilibrium throughout the process. The rapid and uneven changes in pressure and temperature inside the system lead to a less efficient distribution of energy and ultimately result in a lower work output. Quasi-equilibrium expansion processes, on the other hand, maintain mechanical equilibrium by going through a series of infinitesimally small intermediate states, allowing for a controlled and efficient distribution of energy and work.