1 Fundamental concepts
Thermodynamics describes macroscopic systems in terms of measurable quantities such as temperature, pressure, volume, and composition. Its central aim is to relate energy transfer to the observable behavior of matter. Unlike microscopic theories that track individual particles, thermodynamics uses averaged properties and broad laws that apply across many kinds of physical systems.
1.1 System, surroundings, and boundary
A thermodynamic system is the part of the universe selected for study, while the surroundings are everything outside it. The boundary separates the two and may be real or imaginary, fixed or movable. Depending on the system, energy and matter may or may not cross this boundary.
1.2 State variables and state functions
State variables are quantities that specify the condition of a system at a given moment, such as temperature, pressure, and volume. State functions depend only on the present state, not on how the system arrived there. Examples include internal energy, entropy, and enthalpy. In contrast, quantities like heat and work depend on the path taken during a process.
1.3 Equilibrium
A system is in equilibrium when its macroscopic properties no longer change with time and no driving gradients remain within it. In practice, equilibrium often means several kinds of balance are achieved simultaneously. This idealized condition provides a foundation for defining thermodynamic states.
1.3.1 Thermal equilibrium
Thermal equilibrium exists when temperature is uniform and no net heat flows between parts of a system or between a system and its surroundings. It is the condition associated with the common notion of equal temperature.
1.3.2 Mechanical equilibrium
Mechanical equilibrium occurs when pressure forces are balanced and the system does not undergo bulk acceleration or expansion due to unbalanced stress. A fluid in a container at rest is a typical example.
1.3.3 Chemical equilibrium
Chemical equilibrium is reached when the rates of forward and reverse chemical change are equal and the composition remains constant. At this point, there is no net tendency for reaction or diffusion driven by concentration differences.
1.4 Processes and paths
A process is a change from one thermodynamic state to another. The sequence of intermediate states defines the path, which matters for quantities such as heat and work. Different paths can connect the same initial and final states while transferring different amounts of energy.
1.4.1 Quasi-static processes
A quasi-static process proceeds slowly enough that the system remains close to equilibrium throughout. This idealization makes it possible to describe the process using a succession of well-defined states.
1.4.2 Reversible and irreversible processes
A reversible process can, in principle, be reversed without leaving any net change in the system and surroundings. Real processes are irreversible because of friction, finite temperature differences, viscosity, diffusion, and other dissipative effects. Irreversibility is closely linked to entropy production.
1.5 Energy, heat, and work
Energy in thermodynamics is the capacity to do work or transfer heat. Heat is energy transferred because of a temperature difference, while work is energy transferred by a generalized force acting through a displacement or change in a parameter. These are not properties contained in a system, but modes of energy exchange.
2 Laws of thermodynamics
The laws of thermodynamics provide the basic constraints governing energy, equilibrium, and spontaneity. Together they establish a coherent framework for understanding all thermodynamic systems, from engines to chemical reactions.
2.1 Zeroth law
The zeroth law states that if system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other. This law justifies the concept of temperature and the use of thermometers.
2.2 First law
The first law expresses conservation of energy in thermodynamic form. It states that the change in a system’s internal energy equals heat added to the system minus work done by the system, using a common sign convention.
2.2.1 Conservation of energy
Energy cannot be created or destroyed, only transferred or transformed. In thermodynamics, this principle applies to the total energy of a closed system and its surroundings.
2.2.2 Internal energy
Internal energy is the energy associated with the microscopic motions and interactions of the constituents of a system. It excludes the macroscopic kinetic and potential energy of the system as a whole.
2.2.3 Enthalpy
Enthalpy is defined as internal energy plus the product of pressure and volume. It is especially useful for processes occurring at constant pressure, such as many chemical and atmospheric changes.
2.3 Second law
The second law introduces the concept of entropy and determines the preferred direction of natural processes. It shows that although energy is conserved, its ability to do useful work becomes more restricted in real transformations.
2.3.1 Entropy
Entropy is a state function that measures the dispersal of energy and the number of microscopic arrangements compatible with a macroscopic state. For isolated systems, entropy does not decrease.
2.3.2 Direction of spontaneous processes
Spontaneous processes occur in the direction that increases the total entropy of the universe, or, under suitable conditions, decreases the relevant free energy of the system. Examples include heat flow from hot to cold and mixing of substances.
2.3.3 Heat engines and refrigerators
A heat engine converts part of the heat taken from a high-temperature source into work while rejecting the remainder to a lower-temperature sink. A refrigerator and a heat pump use work input to move heat from a colder region to a warmer one. Both are constrained by the second law, which limits their efficiency.
2.4 Third law
The third law states that the entropy of a perfect crystal approaches a minimum value as temperature approaches absolute zero. It provides a reference point for absolute entropy and clarifies the behavior of matter at very low temperatures.
2.4.1 Absolute entropy
Absolute entropy is the entropy of a substance measured relative to the third-law reference state. It can be determined by integrating heat capacity data over temperature, along with contributions from phase changes.
2.4.2 Behavior near absolute zero
Near absolute zero, many substances show sharply reduced thermal motion and unusual quantum behavior. Heat capacities tend to decrease, and reaching absolute zero exactly is not achievable by finite steps.
3 Thermodynamic properties
Thermodynamic properties are measurable characteristics that describe the state of a system. They can be used individually or combined into derived quantities that simplify the analysis of processes and equilibria.
3.1 Intensive and extensive properties
Intensive properties do not depend on system size, such as temperature and pressure. Extensive properties scale with the amount of substance, such as mass, volume, and total entropy. Ratios of extensive quantities, like density, are often intensive.
3.2 Equation of state
An equation of state is a mathematical relation among thermodynamic variables that characterizes a substance or class of substances. The ideal gas law is a familiar example, though real materials often require more complex descriptions.
3.3 Specific heat capacity
Specific heat capacity is the heat required to raise the temperature of a unit mass or amount of substance by one degree. It may vary with temperature, pressure, and phase, and it plays a major role in calculating energy changes.
3.4 Thermodynamic potentials
Thermodynamic potentials are functions designed to make equilibrium and spontaneity criteria easier to apply under different constraints. They are especially valuable when certain variables, such as temperature or pressure, remain fixed.
3.4.1 Helmholtz free energy
Helmholtz free energy combines internal energy with entropy weighted by temperature. It is useful for systems at fixed temperature and volume, where decreases in this potential indicate spontaneous change.
3.4.2 Gibbs free energy
Gibbs free energy combines enthalpy and entropy and is central to chemistry and phase stability. At constant temperature and pressure, spontaneous processes proceed toward lower Gibbs free energy.
3.4.3 Internal energy formulation
The internal energy formulation expresses thermodynamic relations in terms of entropy, volume, and other natural variables associated with internal energy. It provides a compact description of equilibrium properties.
3.4.4 Enthalpy formulation
The enthalpy formulation is convenient for constant-pressure conditions and chemical reactions. It relates changes in heat content to temperature, composition, and other state variables.
4 Classical thermodynamics
Classical thermodynamics treats matter as a continuum and focuses on bulk properties rather than molecular detail. It offers powerful tools for analyzing fluids, solids, phase change, and chemical systems.
4.1 Simple compressible systems
A simple compressible system is one in which the work interaction is mainly due to changes in volume under pressure. This idealization is widely used for gases and liquids in pistons, chambers, and containers.
4.2 Phase transitions
Phase transitions are transformations between different states of matter, such as solid, liquid, and gas. They involve changes in structure and thermodynamic properties, often with absorption or release of latent heat.
4.2.1 Melting and boiling
Melting converts a solid into a liquid, while boiling converts a liquid into a gas. Both processes occur at characteristic conditions for a given substance and pressure.
4.2.2 Critical point
The critical point is the end of the liquid-vapor coexistence curve, beyond which distinct liquid and gas phases no longer exist. Near this point, properties can change rapidly and fluid behavior becomes unusual.
4.3 Chemical thermodynamics
Chemical thermodynamics applies thermodynamic principles to reactions, phase stability, and composition changes. It helps predict whether a reaction can occur and under what conditions it will be favored.
4.3.1 Chemical potential
Chemical potential is the partial molar free energy of a component in a mixture. It governs diffusion, phase equilibrium, and chemical reaction driving forces.
4.3.2 Reaction spontaneity
Reaction spontaneity depends on the balance of enthalpy, entropy, and temperature, often summarized through Gibbs free energy change. A negative free energy change indicates a thermodynamically favored direction under specified conditions.
4.4 Mixtures and solutions
Mixtures contain more than one component, and solutions are homogeneous mixtures in which one substance is dispersed at the molecular level in another. Their thermodynamics involves composition, partial properties, and deviations from ideal behavior.
5 Statistical thermodynamics
Statistical thermodynamics connects macroscopic thermodynamic laws with the behavior of many microscopic particles. It explains how averages over particle states give rise to temperature, entropy, and other bulk quantities.
5.1 Microscopic interpretation of thermodynamic quantities
Macroscopic properties emerge from the collective behavior of atoms and molecules. Temperature reflects average kinetic energy, while entropy relates to the number of accessible microscopic arrangements.
5.2 Microstates and macrostates
A macrostate is defined by macroscopic variables such as energy, volume, and particle number. A microstate specifies the exact microscopic configuration consistent with that macrostate. Many microstates can correspond to the same macrostate.
5.3 Boltzmann entropy
Boltzmann entropy links entropy to the number of microstates available to a system. The larger the number of compatible microstates, the greater the entropy.
5.4 Partition function
The partition function is a central quantity that encodes the statistical weights of accessible states. From it, one can derive thermodynamic properties such as energy, entropy, and pressure.
5.4.1 Canonical ensemble
The canonical ensemble describes systems in thermal contact with a reservoir at fixed temperature, volume, and particle number. It is widely used for solids, gases, and many equilibrium calculations.
5.4.2 Grand canonical ensemble
The grand canonical ensemble allows both energy and particle exchange with a reservoir. It is especially useful for open systems, adsorption, and many problems in quantum and statistical physics.
5.5 Link to kinetic theory
Kinetic theory explains thermodynamic behavior through molecular motion and collisions. It provides a bridge between statistical mechanics and measurable quantities such as pressure and viscosity.
6 Thermodynamic processes and cycles
Thermodynamic processes are often idealized to study how systems exchange energy under controlled conditions. Cycles are sequences of processes that return a system to its initial state and are essential in power and refrigeration technology.
6.1 Isothermal processes
An isothermal process occurs at constant temperature. For many systems, maintaining constant temperature requires heat exchange with the surroundings.
6.2 Adiabatic processes
An adiabatic process involves no heat exchange with the surroundings. Temperature may still change because work is done on or by the system.
6.3 Isochoric processes
An isochoric process takes place at constant volume. Since no volume change occurs, boundary work is absent in the simplest case.
6.4 Isobaric processes
An isobaric process occurs at constant pressure. Many heating and cooling operations in open environments or constant-pressure vessels approximate this condition.
6.5 Carnot cycle
The Carnot cycle is an ideal reversible cycle consisting of two isothermal and two adiabatic steps. It sets the maximum possible efficiency for a heat engine operating between two temperatures.
6.6 Otto cycle
The Otto cycle models spark-ignition engines through compression, heat addition, expansion, and heat rejection. It is a standard idealization in engine thermodynamics.
6.7 Brayton cycle
The Brayton cycle represents gas turbine engines and includes compression, constant-pressure heat addition, expansion, and heat rejection. It is important in aviation and power generation.
6.8 Rankine cycle
The Rankine cycle is the basis of many steam power plants. It uses phase change of a working fluid to convert heat into mechanical work efficiently.
7 Applications
Thermodynamics is used wherever energy conversion, equilibrium, or phase behavior matters. Its concepts are fundamental in engineering design, natural systems, and laboratory analysis.
7.1 Heat engines
Heat engines convert thermal energy into mechanical work. Their design aims to improve efficiency while respecting thermodynamic limits.
7.2 Refrigeration and heat pumps
Refrigeration systems remove heat from a low-temperature region, while heat pumps transfer heat into a warmer one. Both are widely used in climate control and food preservation.
7.3 Power generation
Power plants use thermodynamic cycles to produce electricity from heat sources such as combustion, nuclear reactions, or solar thermal input. The cycle choice affects efficiency, cost, and operating conditions.
7.4 Atmospheric and climate systems
The atmosphere and oceans are large thermodynamic systems driven by solar energy and radiative exchange. Thermodynamic analysis helps describe convection, cloud formation, and energy transport.
7.5 Biological systems
Living organisms maintain ordered states by exchanging energy and matter with their environment. Thermodynamics helps explain metabolism, membrane transport, and temperature regulation.
7.6 Materials and phase engineering
Thermodynamic principles guide the design of alloys, polymers, ceramics, and other materials. Phase diagrams and free energy calculations are used to control microstructure and processing outcomes.
8 Measurement and experimental methods
Thermodynamic quantities are determined through careful measurement and calibrated instruments. Experimental methods allow theory to be connected with observable data and support the characterization of materials and processes.
8.1 Thermometry
Thermometry is the measurement of temperature using devices that respond predictably to thermal conditions. Common instruments include liquid-in-glass thermometers, resistance sensors, and thermocouples.
8.2 Calorimetry
Calorimetry measures heat transfer during physical or chemical changes. It is used to determine heat capacities, reaction enthalpies, and latent heats.
8.3 Pressure and volume measurement
Pressure and volume are measured with devices such as manometers, gauges, and volumetric apparatus. Accurate measurements are essential for evaluating equations of state and process work.
8.4 Temperature scales
Temperature scales provide standardized ways to express thermal state. Kelvin is the SI base scale for thermodynamics, while Celsius and other scales are used in practical settings.
8.5 Experimental determination of thermodynamic quantities
Thermodynamic quantities are often inferred from measurements of heat, work, pressure, volume, composition, and temperature. Combining experimental data with theoretical relations makes it possible to calculate entropy, free energies, and other properties.