Comparison of different equilibrium states, their defining conditions, and key quantitative measures.
Equilibrium Type	System Description	Condition for Equilibrium	Key Quantitative Measure
Mechanical	Rigid bodies	No relative acceleration	$sum ec{F} = 0$, $sum ec{ au} = 0$
Thermal	Thermodynamic systems in contact	No net heat flow	$T_1 = T_2$
Electrostatic	Conductors	No net charge flow (current)	$V_1 = V_2$ (electric potential)
Phase	Substance in multiple phases	No net phase transformation	Chemical potential $mu_{alpha} = mu_{eta}$
Chemical	Reactive mixture	No net change in composition	Reaction Gibbs energy $Delta_r G = 0$

Source: Engineering Principles

Detailed Equplanations

Mechanical Equilibrium

A system is in mechanical equilibrium when the vector sum of all forces and torques acting on it is zero. This ensures no translational or rotational acceleration. Key Formula:

\sum_{i} \vec{F}_i = 0 \quad \text{and} \quad \sum_{i} \vec{\tau}_i = 0

Two systems are in thermal equilibrium when they are in diathermal contact (allowing heat exchange) and no net energy flows between them. This is the basis for the Zeroth Law of Thermodynamics and defines temperature. Key Formula:

T_A = T_B

where $T_A$ and $T_B$ are the absolute temperatures of the systems.

Electrostatic Equilibrium

Conductors reach electrostatic equilibrium when their charges have redistributed such that the internal electric field is zero, and no net current flows. Key Conditions:

The electric field $\vec{E}$ inside the conductor is zero.
Any net charge resides entirely on the surface.
The electric field just outside the surface is perpendicular to the surface.
The conductor is an equipotential volume ( $V = \text{constant}$ ).

Phase Equilibrium

For a pure substance, phases (e.g., solid, liquid, gas) coexist in equilibrium when the chemical potential ( $\mu$ ) of the substance is identical in each phase. For a phase transition like vaporization, this leads to the Clausius-Clapeyron equation relating vapor pressure to temperature. Key Formula (Clausius-Clapeyron):

\frac{dP}{dT} = \frac{\Delta_{trs} S}{\Delta_{trs} V} = \frac{\Delta_{trs} H}{T \Delta_{trs} V}

Chemical Equilibrium

A closed system reaches chemical equilibrium when the forward and reverse reaction rates are equal, resulting in no net change in the concentrations of reactants and products. It is characterized by the reaction quotient $Q$ reaching the equilibrium constant $K$ . Key Formula (Equilibrium Constant):

\Delta_r G = \Delta_r G^\circ + RT \ln Q

At equilibrium ( $\Delta_r G = 0$ , $Q = K$ ):

\Delta_r G^\circ = -RT \ln K

References

Original Source

Source: engineeringtoolbox.com