Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It grew out of the study of steam engines in the nineteenth century, when engineers and scientists asked how much work could be obtained from a given amount of heat. Unlike mechanics, which deals with individual particles, thermodynamics deals with macroscopic systems - large collections of particles - described by quantities such as pressure, volume, temperature, and internal energy.
The laws of thermodynamics are among the most general statements in all of physics. The zeroth law defines temperature, the first law is the law of conservation of energy, and the second law tells us about the direction of natural processes and the limitations on converting heat into work. This chapter studies these laws, the concept of internal energy and work, and the thermodynamic processes of isothermal, adiabatic, isobaric, and isochoric changes.
Thermodynamics explains how refrigerators, heat engines, and air conditioners work, why energy conversions are never perfectly efficient, and why the universe appears to have an irreversible direction of time. It connects the macroscopic behaviour of gases to their microscopic structure through the kinetic theory in the next chapter.
A system is a specific portion of matter under study, and its surroundings are everything outside it. A system can be open (exchanging both matter and energy with surroundings), closed (exchanging energy but not matter), or isolated (exchanging neither). The state of a system is described by its macroscopic variables such as pressure, volume, and temperature.
Two systems are in thermal equilibrium when they are at the same temperature and no heat flows between them. The zeroth law of thermodynamics states that if two systems A and B are each in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other. This law establishes temperature as a property common to systems in thermal equilibrium and forms the basis of temperature measurement with a thermometer.
The internal energy U of a system is the sum of the kinetic and potential energies of all its molecules. It depends only on the state of the system. Heat Q and work W are not properties of the system but are energy in transit; their values depend on the path taken between two states.
The first law of thermodynamics is the law of conservation of energy applied to a thermodynamic system. It states that when a system undergoes a change, the heat supplied to the system equals the change in its internal energy plus the work done by the system:
delta Q = delta U + delta W
Here delta Q is the heat absorbed by the system, delta U is the change in internal energy, and delta W is the work done by the system on its surroundings. The SI unit of all these quantities is the joule.
The first law implies that a system's internal energy can be changed either by heating it or by doing work on it. For an isolated system, delta Q = 0 and delta W = 0, so the internal energy is constant. The first law also means that a perpetual motion machine of the first kind - a machine that produces work without any energy input - is impossible.
When a gas expands, it does work on its surroundings. If a gas at pressure P expands by a small volume delta V, the work done by the gas is:
delta W = P * delta V
For a finite expansion from volume V1 to V2, the total work done is:
W = integral of P dV from V1 to V2
Geometrically, this work equals the area under the pressure-volume (P-V) curve between the initial and final volumes. The work done depends on the path of the process, not just on the initial and final states. This is why work is a path function, not a state function.
For a process at constant pressure (isobaric), the work done is W = P(V2 - V1). For an isochoric process (constant volume), no work is done because there is no change in volume. The P-V diagram is an essential tool for visualising thermodynamic processes.
A gas has two specific heats. The molar specific heat at constant volume, Cv, is the heat required to raise the temperature of one mole of gas by one kelvin while keeping its volume constant. The molar specific heat at constant pressure, Cp, is the corresponding quantity when pressure is held constant. Since a gas heated at constant pressure does work as it expands, Cp is greater than Cv.
The two specific heats are related by Mayer's relation:
Cp - Cv = R
where R is the universal gas constant, 8.314 J/mol K. The ratio of the two specific heats is denoted gamma:
gamma = Cp / Cv
For a monatomic gas, Cv = (3/2)R and Cp = (5/2)R, so gamma = 5/3. For a diatomic gas such as nitrogen or oxygen, Cv = (5/2)R and Cp = (7/2)R, giving gamma = 7/5.
An isothermal process is one that occurs at constant temperature. For an ideal gas, this implies PV = constant, so the P-V curve is a hyperbola. The work done by n moles of an ideal gas in an isothermal expansion from volume V1 to V2 at temperature T is:
W = n R T ln(V2 / V1)
In an isothermal process, the internal energy does not change (for an ideal gas), so the heat absorbed equals the work done.
An adiabatic process is one in which no heat is exchanged with the surroundings (delta Q = 0). For an ideal gas, the relation between pressure and volume is:
P V^gamma = constant
The work done in an adiabatic process comes entirely from the change in internal energy, so the temperature changes. An isobaric process occurs at constant pressure, and an isochoric process at constant volume. Rapid processes such as sound propagation in a gas are nearly adiabatic.
A heat engine is a device that converts heat into work. It operates between a hot reservoir at temperature T1 and a cold reservoir at temperature T2, absorbing heat Q1 from the hot reservoir, doing work W, and rejecting heat Q2 to the cold reservoir. The efficiency of the engine is:
efficiency = W / Q1 = 1 - Q2 / Q1
A refrigerator is a heat engine running in reverse. It absorbs heat Q2 from the cold reservoir (the interior) and ejects heat Q1 to the hot reservoir (the room), with work W supplied. The coefficient of performance (COP) of a refrigerator is:
COP = Q2 / W
Both devices obey the first law: Q1 = W + Q2.
The first law does not tell us whether a process can occur; it only requires energy conservation. The second law of thermodynamics specifies the direction of natural processes. Its Kelvin-Planck statement says that it is impossible to construct a heat engine that converts all the heat absorbed into work without rejecting some heat to a colder reservoir. Its Clausius statement says that heat cannot flow spontaneously from a colder body to a hotter body without external work being done.
The second law implies that no engine operating between two given temperatures can be more efficient than a Carnot engine, which operates between the two temperatures reversibly. The Carnot efficiency is:
efficiency = 1 - T2 / T1
where the temperatures are on the absolute (Kelvin) scale. The second law also introduces the concept of entropy, a measure of disorder. In any natural process, the total entropy of a system and its surroundings never decreases; it increases for irreversible processes.
| Law | Statement |
|---|---|
| Zeroth law | Systems in thermal equilibrium with a third are in equilibrium with each other |
| First law | delta Q = delta U + delta W |
| Second law | Heat cannot be completely converted to work; entropy never decreases |
| Kelvin-Planck | No engine can convert all heat into work |
| Clausius | Heat does not flow spontaneously from cold to hot |
| Process | Condition | P-V Relation |
|---|---|---|
| Isothermal | T constant | PV = constant |
| Adiabatic | Q = 0 | PV^gamma = constant |
| Isobaric | P constant | V/T = constant |
| Isochoric | V constant | P/T = constant |
In this chapter we studied the laws of thermodynamics. The zeroth law established temperature, the first law delta Q = delta U + delta W expressed conservation of energy, and the second law set the direction of natural processes and the limit on engine efficiency. We learned how a gas does work, W = integral P dV, and how the specific heats Cp and Cv of a gas are related by Cp - Cv = R. The isothermal, adiabatic, isobaric, and isochoric processes were described by their P-V relations, and heat engines and refrigerators were analysed through their efficiencies and coefficients of performance. The Carnot efficiency 1 - T2/T1 gives the theoretical upper limit for engines. Thermodynamics now connects naturally to the kinetic theory of gases, which explains these macroscopic laws in terms of molecular motion.