Description
The first law of thermodynamics was expressed in two ways by Clausius. One way referred to cyclic processes and the inputs and outputs of the system, but did not refer to increments in the internal state of the system. The other way referred to any incremental change in the internal state of the system, and did not expect the process to be cyclic. A cyclic process is one which can be repeated indefinitely often and still eventually leave the system in its original state.
In each repetition of a cyclic process, the work done by the system is proportional to the heat consumed by the system. In a cyclic process in which the system does work on its surroundings, it is necessary that some heat be taken in by the system and some be put out, and the difference is the heat consumed by the system in the process. The constant of proportionality is universal and independent of the system and was measured by James Joule in 1845 and 1847, who described it as the mechanical equivalent of heat.
In any incremental process, the change in the internal energy is considered due to a combination of heat added to the system and work done by the system. Taking as an infinitesimal (differential) change in internal energy, one writes
where and are infinitesimal amounts of heat supplied to the system by its surroundings and work done by the system on its surroundings, respectively. This sign convention is implicit in Clausius' statement of the law given above, and is consistent with the use of thermodynamics to study heat engines which provide useful work, which is regarded as positive.
In chemistry, however, it is conventional to use the IUPAC convention where the first law is formulated in terms of the work done on the system. With this alternate sign convention for work, the first law for a closed system may be written:
This convention follows physicists such as Max Planck, and considers all net energy transfers to the system as positive and all net energy transfers from the system as negative, independently of any use for the system as an engine or otherwise.
When a system expands in a quasistatic process, the work done by the system on the environment is the product, P dV, of pressure, P, and volume change, dV, whereas the work done on the system is -P dV. Using either sign convention for work, the change in internal energy of the system is:
Work and heat are expressions of actual physical processes which supply or remove energy, while is a mathematical abstraction that keeps account of the exchanges of energy that befall the system. Thus the term heat for means that amount of energy added or removed by conduction of heat or by thermal radiation, rather than referring to a form of energy within the system. Likewise, work energy for means "that amount of energy gained or lost as the result of work". Internal energy is a property of the system whereas work done and heat supplied are not. A significant result of this distinction is that a given internal energy change can be achieved by, in principle, many combinations of heat and work.
The internal energy of a system is not uniquely defined. It is defined only up to an arbitrary additive constant of integration, which can be adjusted to give arbitrary reference zero levels. This non-uniqueness is in keeping with the abstract mathematical nature of the internal energy. The internal energy is stated relative to a conventionally chosen standard reference state of the system.
Read more about this topic: First Law Of Thermodynamics
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