The Four Laws of Thermodynamics

The behavior of a thermodynamic system is summarized in the four laws of thermodynamics

Zeroth law of thermodynamics

If two systems are in thermal equilibrium with a third system, they must be in thermal equilibrium with each other. This law helps define the notion of temperature.

The zeroth law of thermodynamics may also be stated as follows:

If system A and system B are individually in thermal equilibrium with system C, then system A is in thermal equilibrium with system B The zeroth law implies that thermal equilibrium, viewed as a binary relation, is a Euclidean relation. If we assume that the binary relationship is also reflexive, then it follows that thermal equilibrium is an equivalence relation. Equivalence relations are also transitive and symmetric. The symmetric relationship allows one to speak of two systems being "in thermal equilibrium with each other", which gives rise to a simpler statement of the zeroth law:

If two systems are in thermal equilibrium with a third, they are in thermal equilibrium with each other However, this statement requires the implicit assumption of both symmetry and reflexivity, rather than reflexivity alone.

The law is also a statement about measurability. To this effect the law allows the establishment of an empirical parameter, the temperature, as a property of a system such that systems in equilibrium with each other have the same temperature. The notion of transitivity permits a system, for example a gas thermometer, to be used as a device to measure the temperature of another system.

Although the concept of thermodynamic equilibrium is fundamental to thermodynamics, the need to state it explicitly as a law was not widely perceived until Fowler and Planck stated it in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable.

First law of thermodynamics

Heat and work are forms of energy transfer. Energy is invariably conserved but the internal energy of a closed system changes as heat and work are transferred in or out of it.

The first law of thermodynamics may be expressed by several forms of the fundamental thermodynamic relation for a closed system:

Increase in internal energy of a system = heat supplied to the system – work done by the system. U = Q – W

For a thermodynamic cycle, the net heat supplied to the system equals the net work done by the system.

More specifically, the First Law encompasses the following three principles:

 • The law of conservation of energy
This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. The total energy of an isolated system remains the same.

 • The flow of heat is a form of energy transfer.
(In other words, a quantity of heat that flows from a hot object to a cold object can be expressed as an amount of energy being transferred from the hot object to the cold object.)

 • Performing work is a form of energy transfer.
(For example, when a machine lifts a heavy object upwards, some energy is transferred from the machine to the object. The object acquires its energy in the form of gravitational potential energy in this example.)

Second law of thermodynamics

The entropy of any isolated system not in thermal equilibrium almost always increases. Isolated systems spontaneously evolve towards thermal equilibrium—the state of maximum entropy of the system—in a process known as "thermalization".

The second law of thermodynamics asserts the existence of a quantity called the entropy of a system and further states that:
When two isolated systems in separate but nearby regions of space, each in thermodynamic equilibrium in itself (but not necessarily in equilibrium with each other at first) are at some time allowed to interact, breaking the isolation that separates the two systems, allowing them to exchange matter or energy, they will eventually reach a mutual thermodynamic equilibrium. The sum of the entropies of the initial, isolated systems is less than or equal to the entropy of the final combination of exchanging systems. In the process of reaching a new thermodynamic equilibrium, total entropy has increased, or at least has not decreased. It follows that the entropy of an isolated macroscopic system never decreases. The second law states that spontaneous natural processes increase entropy overall, or in another formulation that heat can spontaneously be conducted or radiated only from a higher-temperature region to a lower-temperature region, but not the other way around.

The second law refers to a wide variety of processes, reversible and irreversible. Its main import is to tell about irreversibility.

The prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies of different temperatures are connected with each other by purely thermal connection, conductive or radiative, then heat always flows from the hotter body to the colder one. This fact is part of the basic idea of heat, and is related also to the so-called zeroth law, though the textbooks' statements of the zeroth law are usually reticent about that, because they have been influenced by Carathéodory's basing his axiomatics on the law of conservation of energy and trying to make heat seem a theoretically derivative concept instead of an axiomatically accepted one. Šilahvý (1997) notes that Carathéodory's approach does not work for the description of irreversible processes that involve both heat conduction and conversion of kinetic energy into internal energy by viscosity (which is another prime example of irreversibility), because "the mechanical power and the rate of heating are not expressible as differential forms in the 'external parameters'".

The second law tells also about kinds of irreversibility other than heat transfer, and the notion of entropy is needed to provide that wider scope of the law.

According to the second law of thermodynamics, in a reversible heat transfer, an element of heat transferred, δQ, is the product of the temperature (T), both of the system and of the sources or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy (S)

δQ = TdS

The second law defines entropy, which may be viewed not only as a macroscopic variable of classical thermodynamics, but may also be viewed as a measure of deficiency of physical information about the microscopic details of the motion and configuration of the system, given only predictable experimental reproducibility of bulk or macroscopic behavior as specified by macroscopic variables that allow the distinction to be made between heat and work. More exactly, the law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of entropy between them. The entropy difference tells how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other , which is often a conveniently chosen reference state. It is often convenient to presuppose the reference state and not to explicitly state it. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes. The entropy increase tells how much extra microscopic information is needed to tell the final macroscopically specified state from the initial macroscopically specified state.

Third law of thermodynamics

The entropy of a system approaches a constant value as the temperature approaches zero. The entropy of a system at absolute zero is typically zero, and in all cases is determined only by the number of different ground states it has. Specifically, the entropy of a pure crystalline substance at absolute zero temperature is zero.

The third law of thermodynamics is sometimes stated as follows:

The entropy of a perfect crystal at absolute zero is exactly equal to zero.

At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one state with minimum energy. Entropy is related to the number of possible microstates according to S = kBln(Ω), where S is the entropy of the system, kB Boltzmann's constant, and Ω the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (Ω=1) and ln(1) = 0.

A more general form of the third law that applies to systems such as glasses that may have more than one minimum energy state:

The entropy of a system approaches a constant value as the temperature approaches zero.

The constant value (not necessarily zero) is called the residual entropy of the system.


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