To understand why both conditions of equilibrium are necessary for complete equilibrium, let's first define the two conditions:
Mechanical equilibrium: This condition refers to the absence of any unbalanced forces or the balance of forces acting on a system. In other words, the net force on an object or within a system is zero.
Thermal equilibrium: This condition refers to the absence of a temperature gradient, meaning there is no difference in temperature between different parts of a system. All parts of the system are at the same temperature.
Complete equilibrium occurs when both mechanical equilibrium and thermal equilibrium are satisfied simultaneously. Each condition is necessary to ensure that the system is in a stable and balanced state.
If only mechanical equilibrium is achieved while thermal equilibrium is not, the system could still have energy transfer occurring due to temperature differences. Heat would flow from regions of higher temperature to regions of lower temperature until thermal equilibrium is established. As a result, the system would not be completely stable or in a state of complete equilibrium.
Similarly, if only thermal equilibrium is achieved while mechanical equilibrium is not, there could be unbalanced forces or motion occurring within the system. These forces could cause changes in the system's configuration or result in a change in the system's energy distribution. Again, the system would not be completely stable or in a state of complete equilibrium.
By satisfying both conditions of equilibrium, a system ensures that there are no unbalanced forces acting within it, and there are no temperature gradients present. This state of complete equilibrium represents a stable, balanced, and unchanging condition for the system.
It's worth noting that achieving complete equilibrium is often an idealized concept and may not be fully attainable in real-world systems. However, working towards minimizing imbalances in forces and temperatures can lead to systems that approach equilibrium to a high degree.