Thermodynamics

Thermodynamic Equilibrium

Question

What is thermodynamic equilibrium? Explain the three types of equilibrium that must be achieved for a system to be in thermodynamic equilibrium.

The three types are:

Thermal equilibrium
Mechanical equilibrium
Chemical equilibrium

Definition of Thermodynamic Equilibrium

A system is said to be in thermodynamic equilibrium when its temperature and pressure are the same at all points of the system, there is no velocity gradient, and chemical equilibrium also exists.

In other words, the system must be in equilibrium with respect to temperature, mechanical effects and chemical composition.

\boxed{ \text{Thermodynamic equilibrium} = \text{Thermal equilibrium} + \text{Mechanical equilibrium} + \text{Chemical equilibrium} }

It is only under thermodynamic equilibrium conditions that the properties of a system can be fixed.

Important Note

A system may have the same temperature and pressure throughout but still not be in complete thermodynamic equilibrium if chemical equilibrium has not been achieved.

Such a system can be described as being in a metastable equilibrium condition when temperature and pressure equilibrium exist but chemical equilibrium does not.

\boxed{ \text{Thermodynamic equilibrium requires all necessary equilibrium conditions} }

Detailed Answer

1. Thermal Equilibrium

A system is in thermal equilibrium when its temperature does not change with time and has the same value at all points of the system.

\boxed{ T_1=T_2=T_3=\cdots=T }

Therefore, there is no temperature difference from one point of the system to another.

Since there is no temperature difference, there is no tendency for heat transfer caused by a temperature gradient within the system.

In simple words

Same temperature everywhere and no change of temperature with time = thermal equilibrium.

2. Mechanical Equilibrium

A system is in mechanical equilibrium when there are no unbalanced forces within the system or between the system and its surroundings.

The pressure in the system is the same at all points and does not change with respect to time.

\boxed{ P_1=P_2=P_3=\cdots=P }

Thus, there is no pressure imbalance that would produce motion or mechanical change in the system.

In simple words

No unbalanced force and uniform pressure = mechanical equilibrium.

3. Chemical Equilibrium

A system is in chemical equilibrium when no chemical reaction takes place in the system and the chemical composition remains the same throughout the system.

\boxed{ \text{Chemical composition does not vary with time} }

Therefore, the chemical state of the system remains unchanged with time.

In simple words

No ongoing chemical change and constant chemical composition = chemical equilibrium.

4. Three Conditions for Thermodynamic Equilibrium

For a system to attain thermodynamic equilibrium, the following three equilibrium states must be achieved:

Thermal equilibrium: Temperature is uniform throughout the system and does not change with time.
Mechanical equilibrium: There are no unbalanced forces and pressure is uniform throughout the system and does not change with time.
Chemical equilibrium: No chemical reaction occurs and chemical composition remains unchanged with time.

\boxed{ \begin{aligned} \text{Thermal equilibrium} &\rightarrow \text{Uniform }T\\ \text{Mechanical equilibrium} &\rightarrow \text{Uniform }P\\ \text{Chemical equilibrium} &\rightarrow \text{Constant composition} \end{aligned} }

5. Easy Example

Imagine a gas inside a closed container.

Thermal condition

If the temperature is different at different locations inside the gas, the system is not in thermal equilibrium.

Once the temperature becomes uniform and remains constant with time, thermal equilibrium is achieved.

Mechanical condition

If pressure varies significantly from one location to another and produces unbalanced forces, the system is not in mechanical equilibrium.

When pressure becomes uniform and there are no unbalanced forces, mechanical equilibrium is achieved.

Chemical condition

If a chemical reaction is still changing the composition of the system, chemical equilibrium has not been achieved.

When the chemical composition remains unchanged with time, chemical equilibrium is achieved.

6. Why Are All Three Equilibria Required?

Thermodynamic equilibrium describes a complete equilibrium state of the system. Therefore, satisfying only one or two conditions is not sufficient.

\boxed{ \text{Complete equilibrium} \Rightarrow T=\text{constant}, \quad P=\text{constant}, \quad \text{composition}=\text{constant} }

If any required condition is absent, the system may still undergo a change and its thermodynamic properties cannot be treated as completely fixed.

7. Comparison of the Three Equilibria

\boxed{ \begin{array}{c|c|c} \text{Type} & \text{Main condition} & \text{What remains unchanged?}\\ \hline \text{Thermal} & \text{Uniform temperature} & \text{Temperature}\\ \text{Mechanical} & \text{No unbalanced forces} & \text{Pressure}\\ \text{Chemical} & \text{No chemical reaction} & \text{Chemical composition} \end{array} }

8. Metastable Equilibrium

According to the source material, a system may have temperature and pressure equilibrium but not chemical equilibrium. Such a condition is sometimes referred to as metastable equilibrium.

Therefore, having uniform temperature and pressure alone should not automatically be treated as complete thermodynamic equilibrium.

\boxed{ \text{Thermal + Mechanical equilibrium} \not\Rightarrow \text{Complete thermodynamic equilibrium} }

9. Why Thermodynamic Equilibrium Is Important

Thermodynamic equilibrium is important because the properties of a system can be fixed only under thermodynamic equilibrium conditions.

Once the required equilibrium conditions are satisfied, the system can be described by definite thermodynamic properties such as temperature and pressure.

10. How to Identify the Type of Equilibrium

In an exam, use these keywords:

If the question mentions temperature being the same everywhere, think thermal equilibrium.
If it mentions pressure, unbalanced forces or velocity gradients, think mechanical equilibrium.
If it mentions chemical composition or absence of chemical reaction, think chemical equilibrium.
If all required equilibrium conditions are satisfied, the system is in thermodynamic equilibrium.

Final Answer

A system is in thermodynamic equilibrium when its temperature and pressure are uniform throughout the system, there is no velocity gradient, and chemical equilibrium is also established.

Three types of equilibrium are required:

Thermal equilibrium: Temperature does not change with time and has the same value at all points of the system.
Mechanical equilibrium: There are no unbalanced forces and pressure is the same at all points and does not change with time.
Chemical equilibrium: No chemical reaction takes place and the chemical composition remains unchanged with time.

\boxed{ \text{Thermodynamic equilibrium} = \text{Thermal} + \text{Mechanical} + \text{Chemical equilibrium} }

Quick Revision

Thermodynamic Equilibrium

\boxed{ \text{Thermal + Mechanical + Chemical equilibrium} }

Thermal Equilibrium

\boxed{ T=\text{same everywhere and constant with time} }

Mechanical Equilibrium

\boxed{ P=\text{same everywhere and constant with time} }

Chemical Equilibrium

\boxed{ \text{Chemical composition remains unchanged} }

Exam Tip

Remember the three words:

\boxed{ T\;-\;P\;-\;\text{Composition} }

T → Thermal equilibrium → Temperature

P → Mechanical equilibrium → Pressure

Composition → Chemical equilibrium

If the question asks for thermodynamic equilibrium, do not write only thermal or mechanical equilibrium. Mention all three required conditions.

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