Understanding the Reversibility Condition in the Work Done Formula for Class 11 Thermodynamics

Introduction

In the study of thermodynamics, the formula for work done during a process is given by W P_{text{internal}} dV. This formula is often mistakenly thought to apply to all processes, but it is specifically applicable to reversible processes only. The reason for this limited applicability lies in the principles of thermodynamics, particularly the concept of reversibility and the conditions under which work can be accurately quantified.

Reversible Processes: Definition and Characteristics

A reversible process is one that can be reversed without any change in the system or surroundings. It is considered to occur infinitely slowly, allowing the system to remain in thermodynamic equilibrium at all stages. During a reversible process, the system is in a state of equilibrium with its surroundings, which means that the internal pressure of the system is equal to the external pressure. This equilibrium ensures that the system can be considered to be doing work against a constant pressure.

Pressure Considerations in Reversible Processes

In a reversible process, the internal pressure P_{text{internal}} is well-defined and equal to the external pressure. This is a crucial factor in the work done formula. Since the system is in a state of equilibrium, the internal pressure can be accurately described as the pressure exerted by the system on its surroundings. This allows for the use of the simplified formula W P_{text{internal}} dV to calculate the work done.

The Inapplicability in Irreversible Processes

Irreversible processes, on the other hand, do not adhere to the conditions of equilibrium. During such processes, the system is not in a state of equilibrium, and the internal pressure may differ significantly from the external pressure. Several factors can cause this, such as friction, turbulence, or rapid changes in volume.

These factors introduce discrepancies that make it impossible to accurately apply the formula W P_{text{internal}} dV. In irreversible processes, the system may not be doing work against a constant pressure. Instead, the work done can vary depending on the path taken during the process, leading to a more complex calculation of work done.

Path Dependency and Work Done in Irreversible Processes

For reversible processes, the work done is path-independent, meaning that the amount of work done can be calculated precisely using the internal pressure and the change in volume. In contrast, irreversible processes require a path-dependent approach to determine the work done. In some cases, this may involve integrating the pressure over the volume changes, reflecting the non-equilibrium nature of the process.

Conclusion

In summary, the formula W P_{text{internal}} dV is only valid for reversible processes because it relies on the assumption of equilibrium and constant internal pressure. Reversible processes allow for the simplification of work calculation due to the equilibrium conditions. For irreversible processes, a more rigorous and path-dependent approach is necessary to accurately determine the work done.