Question

Why does a nonquasi-equilibrium compression process require a larger work input than the corresponding quasiequilibrium one?

Short answer

Answer: A nonquasi-equilibrium compression process requires a larger work input because the rapid changes in pressure and volume do not allow the system to maintain a near-equilibrium state throughout the process. This leads to increased resisting forces (pressure) from the system, requiring more work to compress the system. In contrast, a quasi-equilibrium process, where the system remains close to the equilibrium state, results in minimal resisting forces and less work required for compression.

Step-by-step solution

Quasi-equilibrium processes definition

A quasi-equilibrium process is a process whereby the system remains infinitesimally close to the equilibrium throughout the entire process, which allows us to apply the equilibrium state properties at every stage. In a quasi-equilibrium process, the pressure and volume of the system change slowly, and the system can adjust its internal distribution near the equilibrium state at all times.

Nonquasi-equilibrium processes definition

A nonquasi-equilibrium process is a process in which the system does not remain close to the equilibrium state during the process. In this case, the changes in pressure, volume, or temperature occur rapidly, and the system cannot maintain a near-equilibrium state throughout the process.

Work done during compression processes

The work done on a system during a compression process is given by \(W = -\int_{V_1}^{V_2} P\,\mathrm{d}V\), where \(W\) is the work done, \(V_1\) and \(V_2\) are the initial and final volumes respectively, and \(P\) is the pressure. In a quasi-equilibrium process, the pressure is well-defined at every stage, and the integral can be easily calculated. In a nonquasi-equilibrium process, the pressure is not well-defined at all stages, and we have to consider the worst-case scenario in our calculations.

Comparison of work input between quasi-equilibrium and nonquasi-equilibrium processes

Due to their nature, quasi-equilibrium processes always produce the least amount of work required for a process to occur. As the system remains close to the equilibrium state, the resisting force (pressure) is always adjusted to a minimum value, resulting in less work done by the external agent to compress the system. On the other hand, in a nonquasi-equilibrium process, the system does not have an opportunity to adjust its internal distribution properly due to the rapid changes in the pressure and volume. This leads to higher resisting forces (pressure) from the system and, therefore, requires a greater work input to compress the gas. In summary, a nonquasi-equilibrium compression process requires more work input than the corresponding quasiequilibrium one because the pressure and volume change rapidly and the system cannot maintain a near-equilibrium state throughout the process, which results in increased resisting forces, requiring more work to compress the system.