Table of Contents
Laws of Thermodynamics
1. Introduction
Thermodynamics is the branch of physics that studies heat, work, temperature and energy transformations in physical systems.
It explains how energy is transferred, how heat engines operate, why certain processes occur naturally and why no heat engine can convert all supplied heat into useful work.
The laws of thermodynamics provide the fundamental principles governing these processes.
There are four principal laws:
- Zeroth Law of Thermodynamics.
- First Law of Thermodynamics.
- Second Law of Thermodynamics.
- Third Law of Thermodynamics.
Together, these laws form the foundation of thermal science, energy engineering, refrigeration, power generation and physical chemistry.
2. Basic Thermodynamic Concepts
Before studying the laws, it is useful to understand several basic terms.
2.1 Thermodynamic System
A thermodynamic system is a specified quantity of matter or a region in space selected for study.
Examples include:
- Gas inside a cylinder.
- Water inside a boiler.
- Steam inside a turbine.
- Refrigerant inside a refrigerator.
2.2 Surroundings
Everything outside the system that may interact with it is called the surroundings.
2.3 Boundary
The boundary separates a thermodynamic system from its surroundings. It may be real or imaginary, fixed or movable.
2.4 Types of Thermodynamic Systems
| System | Matter exchange | Energy exchange | Example |
|---|---|---|---|
| Open system | Yes | Yes | Steam turbine |
| Closed system | No | Yes | Gas in a sealed piston-cylinder |
| Isolated system | No | No | Idealised perfectly insulated sealed container |
A real thermodynamic system may approximate an isolated system but perfect isolation is an idealisation.
2.5 Thermodynamic State
The thermodynamic state describes the condition of a system in terms of properties such as:
- Pressure.
- Volume.
- Temperature.
- Internal energy.
- Entropy.
2.6 Thermodynamic Process
A thermodynamic process is a change from one state to another.
Examples include:
- Isothermal process.
- Adiabatic process.
- Isobaric process.
- Isochoric process.
3. Zeroth Law of Thermodynamics
The Zeroth Law establishes the concept of temperature and thermal equilibrium.
It states:
If two systems are separately in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.
Suppose systems A and B are each in thermal equilibrium with system C.
Then:
[
T_A=T_C
]
[
T_B=T_C
]
Therefore:
[
T_A=T_B
]
3.1 Importance of the Zeroth Law
The Zeroth Law provides the basis for temperature measurement.
A thermometer reaches thermal equilibrium with an object and indicates its temperature.
It also allows scientists to compare the thermal conditions of different systems using a common reference.
4. First Law of Thermodynamics
The First Law of Thermodynamics is the law of conservation of energy applied to thermodynamic systems.
It states:
Energy cannot be created or destroyed; it can only be transferred or transformed from one form into another.
When heat is supplied to a system, it may increase the system’s internal energy or be used to perform work.
Using the convention that work done by the system is positive:
[
\Delta U=Q-W
]
Where:
- (\Delta U) = change in internal energy
- (Q) = heat supplied to the system
- (W) = work done by the system
4.1 Interpretation
If heat is supplied to a gas:
- Some energy may increase its internal energy.
- Some energy may be used to expand the gas and perform work.
If the system loses heat, its internal energy may decrease unless work or other energy transfers compensate for that loss.
4.2 Alternative Sign Convention
Some textbooks define work done on the system as positive.
Under that convention:
[
\Delta U=Q+W_{\text{on}}
]
Both forms express the same conservation principle. The sign convention must be stated clearly when solving numerical problems.
5. Applications of the First Law
5.1 Heating a Gas
When a gas is heated inside a rigid container, its temperature and internal energy generally increase.
Because the container does not change volume, boundary work is zero.
[
W=0
]
Therefore:
[
\Delta U=Q
]
5.2 Expansion of a Gas
When a gas expands and performs work, part of the energy supplied as heat may be converted into mechanical work.
5.3 Automobile Engines
Fuel energy is converted into thermal energy and mechanical work, with some energy rejected through exhaust gases and cooling systems.
5.4 Electric Heating
Electrical energy is converted into thermal energy in a heating element.
6. Thermodynamic Processes
Four important thermodynamic processes are commonly studied.
6.1 Isothermal Process
An isothermal process occurs at constant temperature.
[
\Delta T=0
]
For an ideal gas, internal energy depends only on temperature. Therefore:
[
\Delta U=0
]
Using the First Law:
[
Q=W
]
The heat supplied to the gas equals the work done by it.
For a reversible isothermal expansion of an ideal gas:
[
W=nRT\ln\left(\frac{V_2}{V_1}\right)
]
6.2 Adiabatic Process
An adiabatic process occurs without heat transfer between the system and surroundings.
[
Q=0
]
Therefore, using the work-done-by-the-system convention:
[
\Delta U=-W
]
For a reversible adiabatic process involving an ideal gas:
[
PV^\gamma=\text{constant}
]
Where:
[
\gamma=\frac{C_p}{C_v}
]
6.3 Isobaric Process
An isobaric process occurs at constant pressure.
[
P=\text{constant}
]
For a gas expanding at constant pressure:
[
W=P\Delta V
]
6.4 Isochoric Process
An isochoric process occurs at constant volume.
[
V=\text{constant}
]
Because volume does not change, boundary work is zero:
[
W=0
]
Therefore:
[
\Delta U=Q
]
7. Second Law of Thermodynamics
The Second Law explains the natural direction of thermodynamic processes and establishes limits on the conversion of heat into work.
It introduces the concept of entropy.
Two classical statements of the Second Law are the Clausius statement and the Kelvin-Planck statement.
7.1 Clausius Statement
The Clausius statement says:
Heat cannot, by itself, flow from a colder body to a hotter body.
A refrigerator can transfer heat from a colder region to a warmer environment, but it requires external work.
7.2 Kelvin-Planck Statement
The Kelvin-Planck statement says:
No cyclic heat engine can convert all the heat it receives from a single thermal reservoir completely into work.
A heat engine must reject some heat to a lower-temperature reservoir.
7.3 Significance of the Second Law
The Second Law explains why:
- Heat flows naturally from hot to cold.
- Refrigerators require external work.
- Real energy conversions involve limitations.
- No practical heat engine can have 100% thermal efficiency.
- Natural processes have a preferred direction.
8. Entropy and the Second Law
Entropy is a thermodynamic state property that measures the dispersal of energy and the number of microscopic arrangements consistent with a system’s macroscopic state.
For a reversible transfer of heat:
[
dS=\frac{\delta Q_{\text{rev}}}{T}
]
Where:
- (dS) = entropy change
- (\delta Q_{\text{rev}}) = infinitesimal reversible heat transfer
- (T) = absolute temperature
The SI unit of entropy is J K(^{-1}).
8.1 Entropy Principle
The Second Law states that the total entropy of an isolated system cannot decrease.
For an isolated system:
[
\Delta S_{\text{total}}\geq0
]
For a reversible process:
[
\Delta S_{\text{total}}=0
]
For an irreversible process:
[
\Delta S_{\text{total}}>0
]
This principle provides a powerful way of identifying the natural direction of processes.
9. Reversible and Irreversible Processes
9.1 Reversible Process
A reversible process is an idealised process that can be reversed through an infinitesimal change without leaving any net change in the system and surroundings.
A truly reversible process requires ideal conditions, including the absence of dissipative effects.
9.2 Irreversible Process
An irreversible process cannot be reversed without leaving changes in the system or surroundings.
Examples include:
- Heat flowing across a finite temperature difference.
- Friction.
- Free expansion of a gas.
- Mixing of different gases.
- Unrestrained diffusion.
Real-world thermodynamic processes are generally irreversible.
10. Third Law of Thermodynamics
The Third Law of Thermodynamics states:
The entropy of a perfect crystal approaches zero as its temperature approaches absolute zero.
Mathematically:
[
\lim_{T\to0}S=0
]
This statement assumes a perfect crystalline substance with a unique ground state.
10.1 Importance of the Third Law
The Third Law:
- Provides a reference for calculating absolute entropy.
- Explains the behaviour of materials near absolute zero.
- Establishes a fundamental limit for cooling.
- Supports low-temperature physics and cryogenic research.
Absolute zero cannot be reached by a finite sequence of ordinary thermodynamic operations.
11. Relationship Among the Four Laws
| Law | Main principle | Key significance |
|---|---|---|
| Zeroth | Thermal equilibrium is transitive | Establishes temperature |
| First | Energy is conserved | Relates heat, work and internal energy |
| Second | Entropy of an isolated system cannot decrease | Determines process direction and efficiency limits |
| Third | Entropy of a perfect crystal approaches zero at absolute zero | Establishes absolute entropy reference |
12. Important Applications of Thermodynamics
12.1 Power Stations
Thermodynamic principles explain the conversion of heat energy into mechanical and electrical energy.
12.2 Refrigerators
The Second Law explains why external work is needed to transfer heat from a colder region to a warmer environment.
12.3 Air Conditioning
Air-conditioning systems use thermodynamic cycles to remove heat from indoor spaces.
12.4 Automobile Engines
The First and Second Laws help analyse fuel-energy conversion, work output and waste heat.
12.5 Industrial Processes
Thermodynamics is used to evaluate heating, cooling, compression, expansion and energy efficiency in industrial systems.
13. Worked Examples
Example 1: Application of the First Law
A gas receives 500 J of heat and performs 200 J of work. Calculate the change in its internal energy.
Using:
[
\Delta U=Q-W
]
[
\Delta U=500-200
]
[
\boxed{\Delta U=300\ \text{J}}
]
The internal energy increases by 300 J.
Example 2: Isochoric Heating
A gas receives 800 J of heat in a rigid container. Calculate the change in internal energy.
Since volume is constant:
[
W=0
]
Using:
[
\Delta U=Q-W
]
[
\Delta U=800-0
]
[
\boxed{\Delta U=800\ \text{J}}
]
Example 3: Adiabatic Expansion
A gas performs 250 J of work during an adiabatic expansion. Calculate its change in internal energy.
Since:
[
Q=0
]
Using:
[
\Delta U=Q-W
]
[
\Delta U=0-250
]
[
\boxed{\Delta U=-250\ \text{J}}
]
The internal energy decreases by 250 J.
14. Common Examination Mistakes
- Confusing the First Law with the Second Law.
- Assuming the First Law alone determines the natural direction of heat flow.
- Forgetting that the Kelvin-Planck statement rules out complete conversion of heat from a single reservoir into work in a cycle.
- Assuming that adiabatic means constant temperature. It means no heat transfer.
- Assuming that isothermal means no heat transfer. Heat may be transferred during an isothermal process.
- Forgetting to state the sign convention for work.
- Assuming that entropy must always increase in every individual system. The total entropy of an isolated system cannot decrease.
36 Key Takeaways for Exams
- Thermodynamics studies heat, work, temperature and energy transformations.
- A thermodynamic system is the selected matter or region being studied.
- The surroundings are everything outside the system.
- An open system exchanges both matter and energy.
- A closed system exchanges energy but not matter.
- An isolated system exchanges neither matter nor energy.
- The Zeroth Law establishes the concept of temperature.
- The First Law expresses conservation of energy.
- The First Law is written as (\Delta U=Q-W) when work done by the system is positive.
- Heat supplied to a system can increase internal energy or produce work.
- Work done on a system is treated as positive under the alternative work-on-system convention.
- In an isochoric process, volume remains constant.
- Boundary work is zero in an isochoric process.
- In an isobaric process, pressure remains constant.
- In an isothermal process, temperature remains constant.
- For an ideal gas in an isothermal process, internal energy change is zero.
- In an adiabatic process, no heat is exchanged with the surroundings.
- An adiabatic process does not necessarily occur at constant temperature.
- The Second Law establishes the natural direction of thermodynamic processes.
- The Clausius statement concerns the impossibility of spontaneous heat transfer from cold to hot.
- The Kelvin-Planck statement rules out a cyclic heat engine converting all absorbed heat into work.
- Entropy is a thermodynamic state property.
- Entropy is measured in J K(^{-1}).
- The entropy change for reversible heat transfer is (dS=\delta Q_{\text{rev}}/T).
- The total entropy of an isolated system cannot decrease.
- A reversible process produces no net entropy change in the system and surroundings combined.
- Irreversible processes generate positive total entropy.
- Heat transfer across a finite temperature difference is irreversible.
- Friction is an example of an irreversible process.
- The Third Law concerns the entropy of a perfect crystal near absolute zero.
- The entropy of a perfect crystal approaches zero as temperature approaches 0 K.
- Absolute zero cannot be reached through a finite sequence of ordinary thermodynamic operations.
- The First Law describes energy conservation but does not determine process direction.
- The Second Law explains why real heat engines cannot achieve 100% thermal efficiency.
- Refrigerators require external work to transfer heat from a colder region to a warmer environment.
- The four laws of thermodynamics form the foundation of energy engineering, refrigeration and heat-engine analysis.