First Law of thermodynamics

Joule's experiment found that there was no detectable difference in the final state of the system whether its temperature was raised by doing work on it or by heating it. This shows that heat and work are two different means of changing the temperature of the system. Since energy is defined as the capacity to do work, the work done on the sample of water must have increased its energy. Therefore the heat transferred must also have increased its energy. Joule’s sample of water could have kinetic energy if its center of mass were moving, and it could have gravitational potential energy. The work and heat that Joule added to his system did not change either of these forms of energy, instead it is the internal energy, U which is changing. The system is blind to the mode employed. Heat and work are equivalent ways of changing a system’s internal energy.

Based on the experiments of Rumford, Mayer, Helmholtz, Joule, and many others since the time of Joule, we now state the first law of thermodynamics as it applies to a system whose kinetic and potential energy do not change: For a closed system and for any process that begins and ends with equilibrium states

which states that the infinitesimal increment of the internal energy of the body is equal to the algebraic sum of the infinitesimal amount of heat which it absorbs and the infinitesimal amount of work which is done on it. Integrating we have

An isolated system does not allow for passage of matter or energy into or out of the system. If energy is conserved inside the system, then the total energy U of the system does not change. The explicit statement of this is considered the first law of thermodynamics: For an isolated system, the total energy of the system remains constant. This means that

The energy content of an isolted system is constant: ΔU = 0   for any transformation

The system plus its surroundings compose an isolated system, so the first asserts that a change in energy ΔU of the system is accompanied by a change in energy of the surroundings equal to −ΔU, so the total energy of system plus surroundings remains constant (is conserved). For any process,

Il fatto che l'energia del sistema isolato rimanga sempre costante fa del primo principio una riformulazione del principio di conservazione dell'energia

L'energia non può essere nè creata nè distrutta.

E' bene precisare che il lavoro e il calore sono forme di trasferimento dell'energia piuttosto che forme di energia. Quando il sistema viene messo in contatto con l'ambiente e tra questi sussite un gradiente di temperatura, le collisioni tra le molecole dei due provoca un trasferimento di energia cinetica dal corpo caldo a quello fresso. Il calore è quindi lavoro effettuato a livello molecolare.

The first law of thermodynamics states that the time-rate of change of the total energy is equal to the sum of the rate of work done by external forces and the change of heat content per unit time

Where E = energy of mass m, consisting of internal energy and mechanical energy. Internal energy denotes thermodynamics energy associated with microscopic random motions of molecules. Mechanical energy denotes both the kinetic energy and the potential energy associated with observable macroscopic motions (the kinetic energy associated with miscroscopic motion of molecules is part of the internal energy), Q = heat, both that exchanged with the environment and that produced by frictional dissipation and, if any, variation of its volume. W = work done on the mass by external forces.

In most applications of thermodynamics that we shall consider, the system will be at rest and external fields will not be present. Therefore, the macroscopic K and V will be zero, and the total energy E will be equal to the internal energy U.

The first law can be regarded also as a statement of the interconvertibility of heat and work. The law does not place any restrictions on the direction of the process. Namely the conversion of heat to internal energy and internal energy to motion. it is the second law of thermodynamics that provides the restriction on the interconvertibility of energies.

Work and Heat Are Not State Functions, but U Is a State Function

A state function is a property that depends only upon the state of the system, and not upon how the system was brought to that state, or upon the history of the system. Internal energy is an example of a state function. An important mathematical property of a state function is that its differential can be integrated in a normal way:

As the notation suggests, the value of ΔU is independent of the path taken between the initial and final states 1 and 2; it depends only upon the initial and final states through ΔU = U₂ − U₁.

Work and heat are not state functions. For example, the external pressure used to compress a gas can have any value as long as it is large enough to compress the gas. Consequently, the work done on the gas, will depend upon the pressure used to compress the gas. The value of P_ext must exceed the pressure of the gas to compress it. The minimum work required occurs when P_ext is just infinitesimally greater than the pressure of the gas at every stage of the compression, which means that the gas is essentially in equilibrium during the entire compression. In this special but important case, we can replace P_ext by the pressure of the gas (P). When P_ext and P differ only infinitesimally, the process is called a reversible process because the process could be reversed (from compression to expansion) by decreasing the external pressure infinitesimally. Necessarily, a strictly reversible process would require an infinite time to carry out because the process must be adjusted by an infinitesimal amount at each stage. Nevertheless, a reversible process serves as a useful idealized limit.

Just as the reversible isothermal compression of a gas requires the mmtmum amount of work to be done on the gas, a reversible isothermal expansion requires the gas to do a maximum amount of work in the process. In a reversible expansion, the external pressure is infinitesimally less than the pressure of the gas at each stage. If P_ext were any larger, the expansion would not occur. The work involved in the reversible isothermal expansion of an ideal gas is also given by Equation 19.4. Because V₂ > V₁ for expansion, we see that wrev < 0; the gas has done work on the surroundings, in fact, the maximum possible.

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